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THE  PROPERTIES  AND  DESIGN 


OF 


REINFORCED  CONCRETE 


'aw- 


THE   PROPERTIES   AND   DESIGN 

OF 

REINFORCED  CONCRETE 

INSTRUCTIONS,  AUTHORISED  METHODS  OF 
CALCULATION,  EXPERIMENTAL  RESULTS 
AND  REPORTS  BY  THE  FRENCH  GOVERN- 
MENT COMMISSIONS  ON  REINFORCED 
CONCRETE 

TRANSLATED  AND   ABRIDGED 

BY 

NATHANIEL    MARTIN 

Civil 'Engineer, 

A.G.T.C.,  B.Sc.,  A.M.Inst.C.E.  ; 
Lecturer  on  Reinforced  Concrete,  Royal  Technical 
College,  Glasgow 


NEW   YORK 

D.    VAN   NOSTRAND    COMPANY 

TWENTY-FIVE   PARK   PLACE 

1912 


AUTHOR'S  PEEFACE 

IN  setting  out  to  study  the  properties  and  the  applications  of  such  a  com- 
paratively new  material  as  Reinforced  Concrete,  one  is  led  to  consider  the  possible 
sources  of  information  and  their  nature.  The  fact  should  be  kept  in  mind  that, 
from  certain  points  of  view,  the  study  of  much  successful  practice  is  frequently  not 
so  fruitful  as  the  study  of  some  examples  where  failure  took  place  or  of  full-sized 
structures  tested  to  destruction. 

A  considerable  amount  of  experimental  work  has  been  done  and  a  vast  number 
of  reinforced  concrete  structures  successfully  carried  out  in  America,  of  which  the 
records  are  in  English.  In  Germany,  Italy,  and  Austria  a  considerable  amount  of 
both  experimental  and  practical  work  has  been  done.  In  Great  Britain  the  volume 
of  reinforced  concrete  construction  is  steadily  growing,  but  very  little  experimental 
research  on  the  properties  of  the  material  has  been  made  in  this  country.  It  is 
undoubtedly  to  France  and  to  French  literature  that  a  student  must  turn  for  the 
most  concise  and  authoritative  information  on  the  subject. 

Reinforced  Concrete  had  its  origin  in  France.  French  constructors  were 
accumulating  experience  of  its  properties,  and  research  was  being  carried  on  by 
French  engineers  very  many  years  before  the  material  came  to  be  regarded  as  a 
practical  proposition  in  other  countries.  Consequently,  the  Commission  appointed 
in  December,  1900,  by  the  French  Minister  of  Public  Works  embraced  a  group  of 
engineers  whose  experience  in  this  material  was  unrivalled.  The  work  of  this 
Commission,  extending  over  the  succeeding  six  years,  included  a  series  of  experiments, 
simple  in  detail  and  comprehensive  in  range,  and  directed  not  to  the  solution  of 
academical  minutiae,  but  to  the  obtaining  of  results  immediately  applicable  to  practice. 
The  report  of  the  Commission  contains  the  results  of  the  tests  on  experimental 
structures  and  of  the  tests  to  destruction  of  several  of  the  structures  of  the  Paris 
Exhibition  of  1 900.  It  is  unique  in  the  literature  of  Reinforced  Concrete,  containing 
as  it  does  all  the  necessary  scientific  data,  based  on  first-hand  observations,  for  the 
design  of  reinforced  concrete  structures,  with  the  observations  thereon  of  a  group 
of  engineers  of  the  widest  and  most  mature  experience  obtainable.  The  instructions 
are  characteristically  French  in  their  clearness  and  boldness — a  boldness  derived 
from  intimate  knowledge,  and  entirely  justified  by  results. 

The  report  has  been  much  quoted  and  extracts  have  appeared  from  time  to 
time  in  various  English  books  and  periodicals,  but  a  complete  survey  of  the  work 
of  the  Commission  was  to  be  obtained  only  from  the  French  edition.  The  translator 
has  thought  that  a  useful  purpose  might  be  served  by  an  abridged  English  edition 
which  would  enable  professional  men  with  limited  time  to  acquaint  themselves  with 
the  scope  of  the  work  of  the  Commission  and  to  have  the  results  at  hand  in  readily 
accessible  form.  It  will  also  guide  the  research  student  to  the  detailed  records 
of  methods  and  results  to  be  found  in  the  French  edition,  and  at  the  same  time  form 
one  of  the  easiest  avenues  of  approach  for  those  who  wish  to  make  a  systematic 
study  of  the  properties  and  applications  of  Reinforced  Concrete. 

NATHANIEL  MARTIN. 

GLASGOW, 

December,  1911. 


PKEFACE 

THE  rapidity  of  the  development  of  reinforced  concrete  structures,  the 
principle  of  which  was  indicated  by  Monier  in  1877,  is  well  known.  Thanks  to 
the  initiative  of  some  bold  and  skilful  constructors,  a  considerable  number  of 
applications  of  Reinforced  Concrete  had  already  been  made  when  on  December  19, 
1900,  the  French  Minister  of  Public  Works  instituted  a  Commission  to  study  the 
question  from  the  point  of  view  of  his  Administration. 

Notwithstanding  the  already  numerous  experiments,  the  properties  of  the 
new  material  were  still  imperfectly  known,  and  the  methods  of  calculation 
followed  by  different  constructors  presented  essential  differences  and  even  absolute 
contradictions. 

The  elementary  properties  of  Reinforced  Concrete  were  incompletely  investi- 
gated, and  it  was  unknown  in  what  measure  these  properties  permitted  application 
to  the  new  material  of  the  principles  and  the  results  which  had  been  laboriously 
acquired  for  metallic  structures,  and  which  constituted  the  classic  science  of  the 
Resistance  of  Materials. 

The  Commission  decided  that  they  ought  first  to  study  the  elementary 
properties  of  Reinforced  Concrete,  reserving  for  later  research,  in  the  light 
of  these  properties,  the  interpretation  of  the  complex  phenomena  arising  in 
structures. 

The  following  are  some  of  the  facts  established  and  results  obtained  by  the 
Commission  : — 

Experiments  of  several  months'  duration  have  shown  the  importance  of  the 
contraction,  denied  by  certain  constructors,  which  occurs  in  concrete,  not  only  at 
the  end  of  the  period  of  setting  but  also  during  a  long  period  of  hardening,  and 
which  influences  the  distribution  of  the  stresses  between  the  concrete  and  the 
metal.  The  constructor  ought  to  make  the  necessary  arrangements  to  avoid  the 
undesirable  consequences  this  contraction  may  produce. 

The  study  of  elasticity  is  the  basis  of  that  of  stress.  The  Commission  made 
an  important  contribution  to  the  former,  and  verified  for  the  first  time  the  exacti- 
tude of  the  law  announced  by  one  of  its  members  concerning  concrete  under 
tension.  The  modulus  of  elasticity  of  concrete  under  tension  varies  according  to 
a  straight  line  law  up  to  a  certain  limit,  and  afterwards  becomes  almost  rigorously 
constant  till  rupture.  The  stronger  the  reinforcement  with  bars  well  distributed 
in  the  tension  areas,  the  longer  is  rupture  postponed. 

The  laws  of  elasticity  of  concrete  in  compression  had  already  been  the  object 
of  numerous  experiments.  The  Commission  made  additional  experiments  without 
revealing  any  new  facts. 

Attention  has  been  drawn  to  the  fact  that  in  compression  members,  the  longi- 
tudinal bars  necessarily  produce  resistances  proportional  to  the  shortenings  which 
the  concrete  with  which  they  are  associated  supports  without  crushing.  Thus 
arises  the  idea  of  the  importance  of  the  ductility  of  the  concrete. 


viii  PREFACE. 

By  varied  experiments,  which  have  confirmed  the  results  announced  by  one  of 
its  members,  the  Commission  has  definitely  proved  that  for  equal  weights  trans- 
verse reinforcements  and  especially  spirals  increase  the  resistance  to  compression  of 
the  concrete  much  more  than  longitudinal  bars  of  the  same  weight.  In  preparing 
the  regulations  for  the  employment  of  transverse  reinforcements  the  French 
Minister  of  Public  Works  may,  at  first  sight,  have  appeared  rather  daring,  but  the 
expediency  of  his  initiative  is  now  demonstrated  by  the  almost  identical  regulations 
on  this  matter  which  have  been  issued  in  Germany,  and  particularly  in  Austria, 
after  the  repetition  of  the  experiments  inaugurated  in  France. 

The  tests  by  the  Commission  have  given  useful  but  too  scanty  information  on 
the  resistance  of  Reinforced  Concrete  to  shear  and  to  torsion. 

The  study  of  flexion  is  of  prime  importance.  The  Commission  has  given  to  it 
a  rational  basis  by  proving  by  numerous  experiments  that  the  conservation  of 
plane  sections,  which  is  the  foundation  of  the  classic  theory  of  bending,  is  realised 
almost  as  exactly  in  Reinforced  Concrete  as  in  metallic  members, 

The  application  to  Reinforced  Concrete  of  the  exact  ideas  of  the  science  of 
flexure,  and  particularly  of  those  of  the  neutral  axis  and  of  the  moment  of  inertia, 
has  thus  been  sanctioned.  Together  with  the  laws  of  elasticity,  they  permit  of  the 
determination  of  the  stresses  which  are  developed  in  statically  indeterminate 
structures.  These  stresses  depend  not  only  on  the  laws  of  statics,  as  in  members 
statically  determinate,  but  also  on  the  deformations. 

Light  has  been  thrown  by  some  interesting  experiments  on  the  question  of  the 
extent  to  which,  from  the  point  of  view  of  resistance  to  compression,  slabs  assist 
the  ribs  with  which  they  are  continuous  and  form  part. 

Structures  in  Reinforced  Concrete — slab,  floor,  footbridge  and  retaining  wall — 
which  were  erected  for  the  Exhibition  of  1900,  were  tested  to  destruction.  Made 
with  care  and  method  these  tests  have  given  useful  information. 

Finally,  the  theoretical  studies  of  the  Commission  following  on  its  experiments 
cleared  up  several  questions  until  then  obscure,  and  have  thus  given  a  new 
impulse  to  the  researches  of  engineers. 

A.  CONSIDERE. 

PARIS, 
June  11,  1912. 


CONTENTS 

INTRODUCTION 

CHAPTER  I 

INSTRUCTIONS  RELATIVE  TO  THE  USE  OF  REINFORCED  CONCRETE 

PAGE 

Imposed  Loads   .        .         .        ... 1 

Limits  of  Stress 1 

Calculations  of  Resistance .         .  2 

Execution  of  Works 2 

Tests  of  Works 3 

CHAPTER  II 

A  CIRCULAR  ISSUED  BY  THE  FRENCH  MINISTRY  OF  PUBLIC  WORKS  IN  EXPLANATION 

OF  THE  INSTRUCTIONS 

List  of  Symbols  used  in  Chapters  II  and  III 5 

On  Imposed  Loads  and  Working  Stresses 6 

On  Calculations  of  Resistance 8 

On  Simple  Compression 9 

On  Compression  with  Bending 9 

On  Simple  Bending     .............  13 

On  Bending  with  Thrust 14 

On  the  Design  of  Slabs       .         .         .         .         .         .         .         .  .         .         .15 

On  Slipping  of  Reinforcements         .         .         .         . 16 

On  Shear  Resistance  .............  16 

On  the  Strength  of  Long  Columns 17 

CHAPTER  III 

REPORT  ON  THE  DRAFT  REGULATIONS  BY  THE  COMMISSION  NOMINATED  BY  THE 
GENERAL  COUNCIL  OF  BRIDGES  AND  ROADS 

A  Discussion  as  to  the  Advisability  of  Sanctioning  the  High  Working  Stresses 

proposed,  with  Observations  on  the  Values  of  "  ra  "  and  "  m'"        .         .         .       19 

CHAPTER    IV 
THE  EXPERIMENTAL  WORK  OF  THE  COMMISSION 

1.  Measurement  of  Contraction  during  Setting  of  Concrete     .....       22 

2.  Measurement  of  Elasticity  of  Concrete  without  Reinforcement   .         .         .         .22 

3.  Determination  of  Resistance  to  Crushing  of  Concrete  prepared  in   different 

Degrees  of  Plasticity 22 

4.  Influence  of  Percentage  of  Reinforcement  on  Stresses  developed  during  Setting      23 

5.  Tension  Tests  23 


x  CONTENTS 

CHAPTEE  IV.— continued  PAGE 

6.  Shearing  Tests      .         ,         .        ,        .         .'       »    ~'.        .        .         .  .  .       25 

7.  Torsion  Tests .  .27 

8.  Measurement  of  Eesistance  to  Slipping  of  Reinforcements  .         .         .  .  .27 

9.  Bending  of  Beams ....  .  .30 

10.  Bending  of  Flat  Slabs <        .         .         .         .         .         .42 

11.  Bending  of  Eibbed  Slabs       .         .         .  .         .         ...         .         .46 

12.  Compression  Tests  of  Columns  and  Prisms  .         .         .         .         .  .         .       48 

13.  Compression  Tests  of  Spiralled  Mortar  and  Concrete    .         .         .         .         .         .59 

14.  Tension  Tests  on  Eeinforced  Concrete  Members 66 

CHAPTEE    V 

THE  REPORT  AND  DRAFT  REGULATIONS  PRESENTED  BY  THE  COMMISSION,  BEING  A 
REVIEW  OF  THE  PRINCIPAL  RESULTS  OF  THE  EXPERIMENTAL  WORK  OF  THE 
COMMISSION 

Variations  in  Volume  resulting  from  the  Setting  of  the  Cement        .  .         .68 

Thermal  Variations  in  Volume 68 

Resistance  and  Deformation  of  Concrete  submitted  to  Tension  .....       69 

Resistance  to  Crushing 69 

Pitch  of  Spirals 76 

Elasticity  of  Concrete  Reinforced  and  without  Reinforcement  .        .  .77 

Deformation  of  Plane  Sections  in  Bending 78 

Application  of  the  Laws  of  Simple  Deformations  to  Bent  Pieces        .         .         .         .79 

Adhesion  of  the  Concrete  to  the  Metal 79 

Resistance  to  Shear 80 

Note  on  the  Results  of  the  Tests  on  the  Works  constructed  for  the  Exhibition  of  1900      80 

CHAPTER  VI 

SOME  CONCLUSIONS  OF  THE  COMMISSION  FROM  THE  STUDY  OF  THE  ELEMENTARY 
PROPERTIES  OF  THE  MATERIALS  CONSTITUTING  REINFORCED  CONCRETE 

Calculations  of  Stresses  and  Deformations 81 

Coefficients  of  Security 81 

Simplification  of  the  Calculations 81 

Members  Compressed  and  Bent 85 

Adhesion  of  the  Metal  to  the  Concrete 87 

Transverse  Reinforcement  of  Members  subject  to  Bending 88 

Empirical  Formulae 89 

Tests 90 

CHAPTER  VII 

NOTES  PRESENTED  BY  M.  CONSIDERE 

A.  Tension  Tests  on  Reinforced  Concrete  : — 

Initial  State 93 

Elongation  without  Cracking  of  the  Concrete 93 

Law  of  Deformation  of  Reinforced  Concrete 93 

Curves  of  Loading  and  Unloading v ...  94 

Effects  of  Tension  on  the  Resistance  and  Elasticity  of  Concrete  to  Compression  94 

Effects  of  Repetition  of  Stress 94 

The  Final  State  after  Unloading 95 


CONTENTS  xi 

CHAPTER  VII.—  continued  PAGE 

B.  Bending  Experiments  on  Large  Reinforced  Concrete  Beams  : — 

Initial  State 96 

Deformation  of  Plane  Sections  during  Bending      ......  96 

Position  of  the  Neutrql  Axis 96 

Law  of  Deformations  of  Reinforced  Concrete 98 

Adhesion  and  Slipping  of  the  Reinforcements 99 

Influence  of  Fissures  on  the  Resistance  of  Compression  Areas         .         .         .100 

C.  Effects  of  Transverse  Reinforcements  : — • 

Bending  Experiments 101 

Tension  Experiments 102 

D.  Resistance  of  Reinforcements  to  Shear         ........  102 

E.  Experiments  on  Ribbed  Slabs 103 

Participation  of  Slabs  in  the  Resistance  of  the  Ribs 104 

F.  Variations  in  Length  of  Bars  of  Metal  buried  in  Concrete  during  Setting  .         .  105 

G.  The  Influence  of  the  Proportion   of    Gauging  Water  on  the  Strength   and 

Elasticity  of  Concrete       .        .        .        .         .        .        .         .        .        .         .106 

H.  The  Effects  of  Direct  and  Repeated  Shocks  on  the  Adhesion  and  Resistance  of 

Concrete  .                                          .  107 


APPENDIX 

PART  I 

Vertically  Imposed  Loads  and  Wind  Loads  on  Metallic  Bridges  as  denned  in  the 

Regulations  of  August  29,  1891 109 

PART  II 
Tests  of  Metallic  Bridges  as  required  by  the  Regulations  of  August  29,  1891    .         .111 

PART  in 

Imposed  Loads  and  Tests  stipulated  in  the  Regulations  of  February  17,  1903,  for 

Metallic  Station  Buildings 112 


BIBLIOGRAPHY  ....  .  ....     113 

INDEX  117 


INTRODUCTION 

THE  Commission  on  Reinforced  Concrete  was  instituted  by  a  Ministerial  order 
dated  December  19,  1900,  and  was  charged  "to  study  the  questions  relative  to 
the  employment  of  Reinforced  Concrete  and  to  proceed  to  the  necessary  researches 
to  determine  as  far  as  possible  the  Regulations  which  might  be  framed  for  the 
employment  in  Public  Works  of  this  mode  of  Construction." 

The  following  gentlemen  constituted  the  Commission  : — Monsieur  Lorieux, 
President ;  Monsieur  Considere,  Reporter ;  MM.  Bechmann,  Harel  de  la  Noe,  Rabut, 
Resal,  Mesnager,  Hartmann,  Boitel,  Hermant,  Gautier,  Coignet,  Hennebique, 
Candlot. 

At  its  first  meeting  on  February  16,  1901,  the  Commission  appointed  three 
Sub-Commissions  to  undertake  preparatory  work. 

The  first  Sub-Commission,  presided  over  by  M.  Rabut,  undertook  the  testing  to 
destruction  of  certain  of  the  reinforced  concrete  structures  of  the  Paris  Exhibition 
of  1900. 

The  second  Sub-Commission,  presided 'over  by  M.  Considere,  was  appointed  to 
study  the  following  questions  : — 

1.  Safe  limits  for  tensile  and  compressive  stresses  in  the  concrete. 

2.  Information  to  be  produced  in  draft  schemes  to  demonstrate  that  the  different 
parts  of  the  works  are  within  these  limits  of  security. 

3.  Time  which  must  elapse  between   completion  of  work  and  application  of 
tests,  conditions  and  duration  of  tests  and  the  nature  of  results  to  be  obtained. 

This  Commission  resorted  to  experimental  methods  in  order  to  give  its  proposi- 
tions an  unassailable  foundation.  It  established  the  programme  of  the  numerous 
tests  carried  out  under  the  direction  of  M.  Mesnager  at  the  Laboratory  of  the 
School  of  Bridges  and  Roads. 

The  third  Sub-Commission,  presided  over  by  M.  Bechmann,  studied  questions 
relative  to 

1.  The  production  and  qualities  of  the  cement,  sand  and  gravel,  the  preliminary 
tests  intended  to  indicate  the  quality  of  the  cement,  the  proportions  of  the  materials, 
the  quantity  of  water  employed,  the  methods  of  mixing,  etc. 

2.  The  qualities  of  the  reinforcement. 

3.  The  practical  limits  of  percentage. 

The  three  Sub-Commissions  had  finished  their  labours  by  the  commencement  of 
1905.  On  April  17,  1905,  the  Commission  nominated  M.  Considere  reporter, 
and  undertook  the  discussion  of  the  results  obtained  by  the  Sub-Commissions. 
Finally,  on  January  19,  1906,  the  Commission  presented  the  following  proposi- 
tions to  the  Minister  of  Public  Works  : — 

1.  Draft  circular  to  accompany   the  regulations  for  structures  in  Reinforced 
Concrete. 

2.  Draft  Regulations  for  structures  in  Reinforced  Concrete. 

3.  Report  in  support  of  these  Regulations,  followed  by  complementary  notes  by 
M.  Considere. 


xiv  INTRODUCTION 

The  Minister  of  Public  Works  further  submitted  the  work  of  the  Commission 
to  the  General  Council  of  Bridges  and  Roads,  on  behalf  of  which  it  was  examined 
by  a  Commission  composed  of  M.  Maurice  Levy,  President,  and  MM.  de  Preaudeau 
and  Vetillart. 

This  Commission  presented  to  the  General  Council  a  new  draft,  which,  after 
some  amendments  arising  out  of  the  discussion,  was  approved  by  the  Council,  and 
accepted  by  the  Minister  of  Public  Works. 

The  arrangement  of  sections  adopted  in  the  French  edition1  has  not  been 
adhered  to,  and  the  regulations,  or  "Instructions"  as  they  are  called,  are  given 
only  in  their  final  form  in  the  English  edition. 

1  "  Experiences,  Kapports  et  Propositions  Instructions  Ministerielles  relatives  a  1'emploi  du 
Be"ton  Arme,"  published  by  H.  Dunod  et  E.  Pinat,  Quai  des  Grands  Augustins  49,  Paris  (6e). 


REINFORCED   CONCRETE 

CHAPTER  I 

INSTRUCTIONS  RELATIVE  TO  THE  USE  OF  REINFORCED  CONCRETE 

PART  I 
DATA  FOR  DESIGN 

A.  Imposed  Loads. 

Article  1. — Bridges  in  reinforced  concrete  shall  be  designed  to  support  the 
vertical  externally  applied  loads  and  the  wind  loads  stipulated  by  the  regulations 
of  August  29,  1891. * 

Article.  2. — Superstructures  in  reinforced  concrete  shall,  unless  exception  can  be 
justified,  be  submitted  to  the  imposed  loads  stipulated  in  the  regulations  of 
February  17,  1903.1 

Article  3. — The  floors  and  other  parts  of  buildings,  retaining  walls,  conduits 
under  pressure  and  all  other  works  in  which  the  public  safety  is  involved  shall  be 
designed  in  view  of  the  greatest  imposed  loads  to  which  they  will  be  exposed  in 
service. 

B.  Limits  of  Stress. 

Article  4. — The  compressive  stress  allowed  in  the  calculations  for  reinforced 
concrete  ought  not  to  exceed  0'28  of  the  crushing  resistance  acquired  by  non- 
reinforced  concrete  of  the  same  composition  after  ninety  days'  setting.  The  estimated 
value  of  this  resistance,  as  measured  on  cubes  of  7*88  inch  side,  shall  be  stated  in 
the  calculations  for  each  project. 

Article  5. — When  the  concrete  is  spiralled,  or  when  transverse  or  oblique 
reinforcements  are  introduced  and  so  arranged  as  to  resist  more  or  less  efficiently 
the  transverse  swelling  of  the  concrete  under  the  influence  of  compression,  the 
limit  of  the  compressive  stress  set  forth  in  the  preceding  article  will  be  increased  in 
a  greater  or  less  degree  depending  on  the  volume  and  the  efficiency  of  the  trans- 
verse reinforcements,  provided  that  the  new  limit,  whatever  the  percentage  of  metal 
employed,  shall  not  exceed  0*60  of  the  resistance  to  crushing  of  the  non-reinforced 
concrete  as  it  is  defined  in  Article  4. 

Article  6. — The  limit  of  stress  in  shear,  in  the  longitudinal  slipping  of  the 
concrete  on  itself  and  in  the  adhesion  of  the  metal  of  the  reinforcements  to  the 
concrete  will  be  O'lO  of  the  limit  of  compressive  stress  defined  in  Article  4. 

1  See  Appendix,  p.  109. 
R.C.  B 


.     . 


n^IJi  REINFORCED   CONCRETE 


Article  7. — The  limit  of  the  compressive  and  tensile  stresses  in  the  metal  of  the 
reinforcements  shall  be  0'50  of  the  apparent  limit  of  elasticity,  as  denned  in  the 
calculations  for  each  project. 

For  members  exposed  to  shocks  or  submitted  to  stresses  alternating  in  sense, 
such  as  in  some  floors,  this  limit  will  be  reduced  to  0'40  of  the  said  apparent  limit 
of  elasticity. 

Article  8. — In  members  submitted  to  very  variable  stresses,  the  limits  of  stress 
defined  above  shall  be  reduced  to  an  extent  depending  on  the  variation  of 
stress.  This  diminution  need  not  exceed  in  any  case  25  per  cent,  of  the  values 
above  stated. 

The  limits  of  stress  shall  also  be  reduced  for  members  exposed  to  causes  of 
fatigue  or  enfeeblement,  of  which  the  calculations  of  resistance  do  not  take  account, 
e.g.,  members  such  as  rail  bearers  exposed  to  violent  dynamic  action. 


PART  II 
CALCULATIONS  OF  RESISTANCE 

Article  9. — In  the  calculations  of  the  resistance  of  works  in  reinforced  concrete 
there  shall  not  only  be  taken  into  account  the  greatest  external  forces,  including  the 
action  of  the  wind  and  snow,  that  the  works  will  have  to  resist,  but  also  the  thermal 
effects  and  the  effects  of  the  contraction  of  the  concrete  in  those  cases  where  the 
concrete  is  prevented  from  contracting  or  expanding  freely  in  the  theoretical  sense 
of  the  word,  or  where  experience  does  not  show  that  they  may  be  regarded  as 
approximately  such. 

Article  1 0. — The  calculations  of  resistance  shall  be  made  according  to  scientific 
methods  resting  on  experimental  data,  and  not  by  empirical  processes.  They  shall 
be  deduced  either  from  the  principles  of  resistance  of  materials  or  from  principles 
offering  at  least  the  same  guarantees  of  exactitude. 

Article  1 1. — The  resistance  of  the  concrete  to  tension  will  be  taken  into  account 
in  the  calculation  of  the  deformations.  To  determine  the  stress,  however,  in  any 
section  this  resistance  shall  be  regarded  as  zero  in  that  section. 

Article  1 2. — It  must  be  ensured  that  compression  members  are  not  exposed  to 
buckling.  That  precaution  may  be  dispensed  with  when  the  ratio  of  the  height  to 
the  least  transverse  dimension  is  less  than  20,  and  where  the  stress  does  not  exceed 
the  limit  specified  in  Article  4. 

Article  13. — The  description  must  indicate  the  qualities  and  the  proportions  of 
the  materials  entering  into  the  composition  of  the  concrete.  The  proportion  of 
water  employed  in  gauging  ought  to  be  supervised  with  care,  and  should  be  only 
sufficient  to  give  the  concrete  the  necessary  plasticity  for  the  proper  covering  of 
the  reinforcements,  and  the  filling  of  all  the  voids. 

PART  III 

EXECUTION  OF  WORKS 

Article  14. — The  framing  and  the  setting  of  the  reinforcements  must  present 
sufficient  rigidity  to  resist  without  sensible  deformation  the  loads  and  the,  shocks  to 
which  they  will  be  exposed  during  the  execution  of  the  work  up  till  the  removal  of 
the  framing. 

Article  15. — Unless  in  exceptional  cases  where  the  mixture  would  be  poured 


INSTRUCTIONS  RELATIVE  TO  USE  OF  REINFORCED  CONCRETE  3 

slow-setting  cement  shall  be  used.  The  concrete  shall  be  rammed  with  the  greatest 
care  in  beds  of  which  the  thickness  will  be  in  proportion  to  the  dimensions  of  the 
aggregate  used  and  the  spacing  of  the  reinforcements,  and  shall  not  exceed 
2  inches  after  ramming,  unless  stones  are  used  as  aggregate. 

Article  16. — The  distances  between  the  reinforcements  themselves- and  to  the 
faces  of  the  frames  shall  be  such  that  they  permit  the  perfect  ramming  of  the 
concrete  and  the  complete  surrounding  of  the  reinforcements  by  the  latter.  The 
distance  between  the  reinforcements  and  the  framing,  even  when  mortar  without 
gravel  or  pebbles  is  used,  ought  always  to  be  at  least  from  0*6  inch  to  0*8  inch 
in  order  to  protect  the  reinforcement  from  the  weather. 

Article  17. — When  specially  shaped  sections  are  employed  for  reinforcements 
instead  of  round  bars,  special  precautions  shall  be  taken  to  ensure  the  complete 
covering  of  the  reinforcements  on  all  their  perimeter,  and  particularly  on  any 
re-entrant  angles. 

Article  18. — When  the  concreting  of  a  reinforced  concrete  member  has  been 
interrupted,  which  should  be  avoided  as  much  as  possible,  the  old  concrete  shall  be 
cleaned  to  the  solid  and  thoroughly  moistened  in  order  that  it  may  be  completely 
saturated  before  fresh  concrete  is  put  in  contact  with  it. 

Article  19. — In  time  of  frost  work  shall  be  suspended  if  efficient  arrangements 
cannot  be  made  to  obviate  harmful  effects.  On  restarting  the  work  all  parts  of 
the  concrete  injured  by  the  frost  shall  be  removed,  and  the  procedure  will  then  be 
as  described  in  the  preceding  article. 

Article  20. — For  fifteen  days  at  least,  after  its  execution  there  shall  be  main- 
tained in  the  concrete  sufficient  humidity  to  ensure  setting  under  good  conditions. 

The  removal  of  the  framing  shall  be  done  without  shock  by  purely  static 
forces  and  only  after  the  concrete  has  acquired  the  necessary  resistance  to  support, 
without  damage,  the  forces  to  which  it  will  be  exposed. 

PART  IV 

TESTS  OF  WORKS 

Article  21. — Works  in  reinforced  concrete  which  concern  the  public  safety  will 
be  tested  after  completion.  The  conditions  of  the  tests  as  well  as  the  interval 
which  must  elapse  before  the  works  are  put  into  service  shall  be  inserted  in  the 
general  conditions  of  the  contract.  The  maximum  deflections  in  the  various  parts 
of  the  works  which  ought  not  to  be  exceeded  shall  also  as  far  as  possible  be  stated 
in  the  general  conditions. 

The  age  that  the  concrete  ought  to  have  at  the  moment  of  the  tests  will  also 
be  fixed  by  the  general  conditions.  It  will  be  at  least  ninety  days  for  large 
works,  forty-five  days  for  works  of  average  importance  and  thirty  days  for  floors. 

Article  22. — The  engineers  shall  record  at  the  time  of  the  tests  not  only 
the  measurements  of  deformation  and  such  other  measurements  as  are  necessary 
for  the  verification  of  the  general  conditions  of  the  contract,  but  also  as  far 
as  possible  any  other  measurements  which  might  be  of  service  to  engineering 
science. 

For  works  of  importance  registering  apparatuses  shall  be  employed. 

Article  23. — Bridges  in  reinforced  concrete  shall  be  tested  in  the  manner 
prescribed  for  metallic  bridges  by  the  regulation  of  August  29,  189 1.1 

1  See  Appendix,  p.  111. 

B  2 


4  REINFORCED   CONCRETE 

If  it  appears  desirable  to  obtain  any  amendments  to  the  prescription  of 
this  regulation,  these  amendments  ought  to  be  justified  and  inserted  in  the  general 
conditions. 

Article  24. — Superstructures  shall  be  tested  in  the  manner  prescribed  by 
the  regulation  of  February  17,  1903,  unless  amendments  are  justified. 

Article  25. — Floors  shall  be  submitted  to  a  test  consisting  of  the  application 
of  the  loads  and  the  superloads  intended,  either  to  the  whole  of  the  floor  or 
at  least  to  an  entire  span. 

The  test  loads  ought  to  remain  in  place  for  at  least  twenty-four  hours,  and 
the  deflections  ought  not  to  increase  at  the  end  of  fifteen  hours. 


LIST   OF   SYMBOLS 


CHAPTER    II 


A  CIRCULAR  ISSUED  BY  THE  FRENCH  MINISTRY  OF  PUBLIC  WORKS  IN  EXPLANATION 
OP  THE  INSTRUCTIONS,  GIVING  DETAILED  METHODS  OF  CALCULATING  RESISTANCES 
AND  CHECKING  DESIGNS  (ABRIDGED) 

LIST  OF  THE  SYMBOLS  USED  IN  CHAPTERS  II  AND  III 


V 
V 

m' 


A 

Ac 
A, 

N 


G 


C 

Y  =  G 
T,  =  G, 
Ye  =  G 

/,,/c 


the  volume  of  the  concrete  in  unit  length  of  prism. 

the  volume  of   the  transverse  or  oblique  reinforcements  in  unit 

length  of  prism, 
coefficient  varying  with  the  spacing  of  the  transverse  or  oblique 

reinforcements  and  the   efficiency  of   the  transverse  connection 

established  between  the  longitudinal  bars, 
the  modulus  of  elasticity  of  steel.     (Young's  modulus.) 
the  modulus  of  elasticity  of  concrete  in  compression. 

E 

the  ratio  -^T. 

&c 

the  equivalent  homogeneous  section  replacing  the  heterogeneous 

section  composed  of  concrete  and  steel, 
the  sectional  area  of  the  concrete, 
the  sectional  area  of  the  longitudinal  reinforcements.      As  A«  is 

generally  small  in  comparison  with  Ac,  Ac  +  A8,  the  total  area,  is 

frequently  taken  instead  of  Ac. 
the  total  compression  normal  to  the  section  applied  at  the  centre  of 

gravity  and  consequently  uniformly  distributed,  or  the  value  of 

the  compression  applied  halfway  between  the  extremities  of  a 

section  if  it  varies  across  the  section, 
the  unital  stress  in  the  concrete. 

the  unital  stress  in  the  reinforcement  on  the  compression  side, 
the  unital  stress  in  the  reinforcement  on  the  tension  side, 
the  centre  of  gravity  of  the  equivalent  homogeneous  section,  the 

position  of  which  is  to  be  found. 

the  known  centre  of  gravity  of  the  longitudinal  reinforcements, 
the  known  centre  of  gravity  of  the  concrete  section, 
the  centre  of  pressure  of  the  resultant  force  on  the  cross  section, 
the  ordinate  of  G  from  an  axis  xx'  chosen  at  will.     (See  Fig.  1.) 
the  ordinate  of  Ga  from  the  axis  xx'.     (See  Fig.  1.) 
the  ordinate  of  Gc  from  the  axis  xx '.     (See  Fig.  1.) 
the  second   moments   of   area    (the   moments   of  inertia)    of   the 

geometrical  sections  of  the  steel  and  concrete  respectively  in  the 

cross  section  of  the  member,  about  the  axis  XGX ' . 
the  second  moment  of  area  of  the  equivalent  homogeneous  section 

about  XGX'. 
the  shear  on  any  section,  i.e.,  the  component,  tangential  to  the 

section,  of  all  the  exterior  forces,  including  the  support  reactions 

which  lie  on  one  side  of  the  section. 


EEINFORCED   CONCRETE 
LIST  OF  THE  SYMBOLS  USED  IN  CHAPTERS  II  AND  III — continued. 


M 


P 

s 

h 

b 

b' 

t 

w 

d 

w' 

d' 


L 
p 

i 
k 

K 


the  bending  moment  applied  to  the  cross  section,  i.e.,  the  sum  of 
the  moments  of  the  exterior  forces  relatively  to  G,  the  centre  of 
gravity  of  the  equivalent  section. 

lie  unital  stress  on  the  concrete  distant  x  from  the  axis  XGX  '. 

the  unital  stress  on  the  steel  distant  x  from  the  axis  XGX  '. 

the  co-ordinate  of  the  centre  of  pressure  (or  point  of  application  of 
relative  to  the  axis  XX'. 

the  distance  from  the  extreme  edge  of  the  concrete  and  from  the 
reinforcement  respectively  to  the  axis  XGX',  reckoned  negative 
when  measured  to  the  side  of  XX'  on  which  the  bending  moment 
produces  tension. 

the  co-ordinate  of  the  neutral  axis  relatively  to  the  axis  XX'  . 

the  radius  of  gyration  of  the  equivalent  section  relatively  to  XX'  . 

the  minimum  radius  of  gyration.  In  a  symmetrical  section  either 
about  the  axis  of  symmetry  or  an  axis  normal  to  the  latter. 

the  imposed  load  per  unit  length  of  span. 

the  effective  span  (centre  to  centre  of  bearings). 

the  overall  depth  of  slab  and  rib. 

the  width  of  the  slab. 

the  width  of  the  rib. 

the  thickness  of  the  slab. 

gross  section  of  the  compression  reinforcement. 

its  mean  distance  to  the  compression  face. 

net  section  of  the  tension  reinforcement. 

its  mean  distance  to  the  tension  face. 

the  distance  of  the  neutral  axis  from  the  compressed  face. 

the  distance  of  the  neutral  axis  from  the  centre  of  pressure  C. 

the  distance  of  the  point  of  application  of  the  resultant  of  the 
exterior  forces  from  the  compressed  face. 

the  spacing  centre  to  centre  of  the  ribs. 

the  perimeter  of  the  longitudinal  reinforcements. 

the  length  of  a  column. 

a  numerical  coefficient  depending  on  the  end  conditions  of  a  column. 

the  "angular  coefficient"  of  the  line  A'B'  in  Fig.  3,  numerically 
M      R 


equal  to 


or 


NOTE. — The  quantities  must  be  expressed  in  the  same  units  throughout.  The  most  generally 
convenient  units  are  the  inch  and  the  lb.,  with  their  derivatives,  the  inch-lb.  and  the  Ib.  per 
square  inch.  These  units  are  applicable  without  conversion  to  the  formulae  throughout  the 
volume. 

Imposed  Loads  and  Working  Stresses. 

Article  3. — At  first  sight  this  article  seems  simply  to  be  the  statement  of 
the  very  evident  necessity  of  designing  a  reinforced  concrete  structure  so  that 
the  elastic  resistances  called  into  play  in  the  various  members  by  the  action 
of  the  external  forces  only  attain  a  determined  fraction  of  those  which  would 
endanger  the  stability  or  the  life  of  the  structure.  This  pre-determined  fraction  is 
called  the  coefficient  of  security  or  factor  of  safety. 

The  article  is  really  directed,  however,  against  a  method  in  use  by  certain 
specialists.  This  consists,  not  in  determining  the  elastic  resistances  called  into 


WORKING   STRESSES 


play  to  balance  the  actual  loads,  but  in  attempting  to  determine  the  proportion 
in  which  it  would  be  necessary  to  imagine  the  external  loads  multiplied  in  order 
to  produce  rupture.  This  coefficient  of  amplification  is  called  by  them  the 
factor  of  safety. 

This  procedure  will  be  disallowed  in  preparing  designs,  as  it  is  held  not 
necessarily  to  offer  a  sufficient  guarantee  of  security.  No  work  has  ever 
perished  by  the  proportional  amplification  of  the  loads,  but  always  by  accidental 
cause  or  by  some  internal  flaw  the  development  of  which  proved  fatal. 

Article  4. — The  following  table  provides  a  comparison  of  working  stresses  in 
compression  allowed  by  foreign  regulations  with  those  permitted  by  the  French 
instructions  : — 

TABLE  No.  1. 


Composition  of  Concrete. 

(For  conversion  1  cubic  foot  of  loose  cement  was  taken 
as  weighing  85  Ibs.) 

Average  crushing  resistance 
in  Ibs.  per  square  inch  esti- 
mated by  the  Commission. 

Working 
stresses 
allowed  by 
Foreign 
Regulations, 
25  per  cent, 
of  (a),  Ibs.  per 
square  inch. 

Working 
stresses 
allowed  by 
French 
Instructions, 
28  per  cent, 
of  (&),  Ibs.  per 
square  inch. 

(a) 
After  -28  days. 

(&) 

After  90  days. 

6  cwts.  cement,  28-7  cubic  feet  of  gravel, 
14-4  cubic  feet  of  sand  or  1  of  cement, 
3*5  of  gravel,  and  1'75  of  sand  by 
measure. 

1520 

2275 

380 

637 

7  cwts.  cement,  28  '7  cubic  feet  of  gravel, 
14*4  cubic  feet  of  sand  or  1  of  cement, 
3-12  of  gravel,  and  T56  of  sand  by 
measure. 

1706 

2560 

426 

717  . 

8  cwts.  cement,  28'  7  cubic  feet  of  gravel, 
14-4  cubic  feet  of  sand  or  1  of  cement, 
2'75  of  gravel,  and  1/37  of  sand  by 
measure. 

1890 

2846 

470 

798 

The  French  instructions  thus  permit  a  working  compressive  stress  of  very 
much  higher  value  than  that  allowed  by  foreign  regulations.  It  is  pointed  out 
that  these  regulations  are  of  earlier  date,  and  when  they  are  modified  the  change 
will,  without  doubt,  be  in  the  direction  of  the  French  figures. 

Article,  5. — When  concrete  is  prevented  from  swelling  laterally  under  a 
longitudinal  compression  by  transverse  or  oblique  reinforcements,  or  by  spiralling, 
the  crushing  resistance  is  augmented. 

Experiments  made  by  the  Commission  indicate  that  transverse  reinforcements 
and  spirals  multiply  the  crushing  resistance  by  the  quantity 

1  +  •»'  y. 

m'  varies  with  the  degree  of  efficiency  of  the  transverse  connections  established 
between  the  longitudinal  bars. 

When  the  transverse  reinforcement  consists  of  ligatures  forming  rectangles  on 
a  transverse  section  of  the  prism,  the  coefficient  might  vary  from  8  to  15,  the 


8  EEINFORCED   CONCRETE 

minimum  value  being  applied  when  the  spacing  of  the  transverse  reinforcements 
attains  a  value  equal  to  the  least  transverse  dimension  of  the  member  considered, 
the  maximum  value  being  applied  when  the  spacing  of  the  transverse  reinforce- 
ments is  reduced  to  at  least  one-third  of  that  dimension. 

When  the  transverse  reinforcement  consists  of  a  spiral  tie,  the  coefficient  might 
vary  from  15  to  32.  The  minimum  should  be  applied  when  the  pitch  of  the 
spirals  is  two-fifths  of  the  least  transverse  dimension  of  the  piece  considered,  and 
the  maximum  when  this  spacing  is  reduced  to 

one-fifth  of  that  dimension  for  a  compression  of  711  Ibs.  per  square  inch, 
one-eighth  of  that  dimension  for  a  compression  of  1,422  Ibs.  per  square  inch. 


Whatever  the  value  of    the  quantity   1  +  —  TT~  or  the  percentage  of  metal, 

the  compressive  stress  must  not  exceed  60  per  cent,  of  the  resistance  of  non-rein- 
forced concrete  as  defined  by  Article  4.  This  ensures  that  the  stress  does  not 
exceed  half  the  value  at  which  superficial  cracking  of  the  concrete  commences, 
which,  according  to  the  experiments  of  the  Commission,  varies  from  25  per  cent,  to 
GO  per  cent.,  depending  on  the  case,  of  that  which  produces  crushing  of  the 
reinforced  concrete. 

Calculations  of  Resistance. 

Article  10.  —  This  article  sets  aside  all  purely  empirical  processes  of  calcula- 
tion. The  principles  of  resistance  of  the  materials  employed  afford  here,  as  in 
ordinary  structures,  more  sure  solutions. 

The  experiments  described  in  Chapter  IV.  show  that  the  principle  of  Navier 
relative  to  the  plane  deformation  of  transverse  sections  is  applicable  within  the 
limits  of  the  experiments.  This,  combined  with  the  application  of  the  principle  of 
the  proportionality  of  stresses  to  the  deformation  suffices,  in  the  case  of  compression 
members. 

Each  heterogeneous  section  may  be  replaced  by  an  equivalent  section  having 
the  same  mass  as  the  real  heterogeneous  section  by  attributing  to  the  parts  of  the 
section  formed  by  the  concrete  a  density  1  and  to  the  parts  formed  by  the  longi- 
tudinal reinforcements1  a  density  m. 

Hypothetically 


This  ratio  within  the  limits  of  the  loads  defined  by  Article  4  is  about  10.  It 
grows  with  the  stress  in  the  concrete  and  might  be  doubled  or  tripled  at  the 
moment  of  rupture,  if  failure  took  place  by  the  crushing  of  the  concrete.  On  the 
other  hand,  it  would  diminish  if  failure  took  place  by  excess  of  load  on  the 
reinforcements. 

This  fact  alone  shows  how  uncertain  would  be  the  calculations  of  resistance 
based  on  the  imaginary  increase  up  to  rupture  of  the  actual  loads,  —  a  method 
previously  referred  to. 

It  is  preferable  to  regard  the  coefficient  m  as  a  figure  derived  from  experience 
and  not  as  representing  exactly  the  ratio  of  the  moduli  of  elasticity  of  the  metal 
and  of  the  concrete  separately  found.  In  every  case  the  experiments  to  determine 
the  modulus  of  elasticity  Ec  were  carried  out  in  non-reinforced  concrete,  and  it  is 

The  transverse  reinforcements  do  not  figure  here.  Their  essential  rdle  has  already  been 
considered  and  allowed  for  by  the  increase  (Article  5)  permitted  in  the  limit  of  crushing  stress 
of  the  concrete.  It  is  in  the  augmentation  of  the  resistance  to  crushing  due  to  the  opposition  to 
lateral  swelling  in  which  their  efficacy  resides. 


CALCULATIONS   OF   RESISTANCE 


doubtful  if  the  value  thus  found  is  the  true  value  of  the  modulus  of  the  concrete  in 
reinforced  members  owing  to  the  difficulty  experienced  in  ramming  the  concrete 
between  the  reinforcements  and  the  moulds. 

It  may  be  taken  that  this  coefficient  might  vary  from  8  to  15.  The  minimum 
value  will  be  applied  when  the  longitudinal  bars  have  a  diameter  equal  to  one-tenth  of 
the  smallest  dimension  of  the  member,  the  transverse  interties  being  spaced  at  this 
latter  dimension  and  the  longitudinal  bars  being  slightly  shorter  than  the 
column.  The  maximum  will  be  applied  when  the  diameter  of  the  longitudinal 
bars  is  one-twentieth  of  the  smallest  dimension  of  the  member  and  the  transverse 
interties  spaced  at  one-third  of  this  same  dimension. 

The  greater  number  of  authors  allow  for  "m"  a  fixed  value,  which  is  often 
taken  equal  to  15.  There  is  thus  attributed  in  many  cases,  without  doubt,  to  the 
metal  a  greater  part  of  the  resistance  than  it  actually  takes,  and  to  the  concrete  a 
less.  Trouble  might  thus  arise  owing  to  the  fact  that  the  stress  in  the  concrete  is 
greater  than  the  calculation  assumes,  and  consequently  the  coefficient  of  security  is 
lower  than  was  intended.  By  varying  "  m  "  as  above  described,  a  more  accurate 
determination  of  the  stresses  is  made,  which  is  necessary  in  view  of  the  high  values 
allowed  in  Article  4. 

Once  the  coefficient  m  has  been  chosen,  the  formulae  to  be  applied  may  easily 
be  put  into  the  classical  form  which  applies  to  a  homogeneous  solid. 


Simple  Compression. 

A  =  Ac  +  m  A, 


•     (2) 


If  Ec  be  given,  A  can  be  calculated  from  it.  Consequently  by  the  help  of  (2),  and 
knowing  the  actual  total  section  of  the  member,  As  the  total  section  of  the  rein- 
forcements, or  — *  the  percentage  reinforcement,  may  be  found. 

Compression  with  Bending. 

When  the  total  compression  N  is  not  uniformly  distributed,  it  is  necessary  to 
consider,  besides  the  area  A  of  the  equivalent  section,  the  position  of  its  centre  of 
gravity  and  its  moment 
of  inertia  (more  properly 
its  second  moment  of  area) 
relative  to  the  axis  passing 
through  its  centre  of 
gravity  and  normal  to  the 
plane  of  bending.  — £- &• 

Fig.  1  is  a  sketch  of 
a  section,  supposed  to  be 
symmetrical  about  an  axis 
y'y  passing  through  its 
centre  of  gravity. 

The  centres  of  gravity 
Gs  and  Gc  of  the  reinforce- 
ment and  of  the  concrete  are  known,  as  are  also  Y8  and  Yc,  their  distances  from 
an  axis  xx1  chosen  at  will,  the  abscissae  Ys  and  Y&  etc.,  being  reckoned  positive 
on  one  side  xxf,  negative  on  the  other. 


10  REINFORCED   CONCRETE 

A,  the  area  of  the  equivalent  section,  is  given  by  (2).  Y  and  the  position  of 
the  axis  XGX'  is  then  determined  from  the  following  equation  ;  — 

A  Y  =  \YC  +  m  A,r.  .  .     (4) 

Is  and  Ic  are  then  calculated,  and  /  is  then  determined  by  equation  (5)  : 

I=le  +  mlt.  .      (5) 

As  previously  pointed  out,  it  is  more  convenient  in  practice  to  deal  with  At,  the 
total  area  of  the  member,  than  with  Ac,  the  area  of  the  geometrical  section  of 
concrete,  and  the  error  thereby  introduced  is,  almost  without  exception,  negligible  : 

A,  =  Ac  +  A,. 

Consequently  we  also  deal  with  Gt  and  /  respectively,  the  centre  of  gravity  of 
the  total  area  of  the  cross  section  and  the  second  moment  of  that  area  relative  to 
an  axis  parallel  to  XGX1  passing  through  Gt. 

Formulae  (2),  (4)  and  (5)  are  then  rewritten 

A  =  A,  +  (m  -  1)  As          .          .          .          .     (2'; 
Ar=Aer<  +  (m-l)A,r,.         .         .         .     (4') 
/=/«  +  At(Y--Yt)*  +  (m-  I)/,          .     (5') 
Now  if  in  addition  to  Ny  there  is  applied  a  bending  moment  Mt 

N   .    M 

HC  =  A  +   7  *        .....  ^     ^ 

and  if  at  the  point  considered  there  is  found  a  longitudinal  reinforcement,  the 
compression  it  would  carry  would  be 

n,  =  m  nc      ......      (6) 

In  (5a)  x  must  be  reckoned  positive  when  it  represents  the  distance  to  points 
lying  to  that  side  of  XGX'  on  which  the  bending  moment  produces  compression. 
For  example,  when  the  bending  moment  produces  compression  between  G  and  K, 
and  tension  between  G  and  D,  then  x  must  be  reckoned  positive  for  all  points 
between  G  and  K  and  negative  for  all  points  between  G  and  D. 

The  maximum  compression  in  the  concrete  will  then  be  given  by  (7)  : 

N   .    M  m 

nc  =  -  +  jxc       .  .     (7) 

Its  least  compression  will  be 

N       M  ,-  N 

*•  =  A  "  7  *•     '  '  ('a) 

The  compressions  in  the  reinforcements  will  be  obtained  by  substituting  the 
appropriate  values  of  x-8  in  (7)  : 

M 


IN       M     \ 

Us  ~  m  \A  ~~  T  x§)  '  '  '    ^ 


It  is  an  essential  condition  for  the  correct  application  of  these  formulae  that 
compression  exists  throughout  the  cross  section,  or  that  in  (7a)  and  (8a)  nc  and  ns 
are  positive,  If  in  these  formulae  the  resultant  stress  was  negative  or  a  tension, 
the  formulae  would  no  longer  apply,  since  the  laws  of  tension  in  concrete  differ 
widely  from  those  expressing  the  phenomena  of  its  compression.  In  that  case  the 
procedure  will  be  as  explained  later. 


CALCULATIONS   OF   RESISTANCE  11 

If  the  centre   of  pressure  of    the  cross   section   considered    were  known,  by 
definition 

M=Nx0  .       (9) 

and 

/  =  A  i*  .     (10) 

we  have 


The  neutral  axis  would  by  definition  be  obtained  when  nc  =  o,  that  is  when 


x'  being  the  coordinate  defining  the  position  of  that  axis. 
Formula  (7  a)  becomes  with  these  notations 


Comparison  of  (12)  and  (13)  indicates  that  there  is  only  compression  throughout 
the  cross  section  when  —  x'  >  %„  that  is  when  the  neutral  axis  falls  outside  the 
section. 

The  preceding  formulae  suppose  that  N  and  M  are  known  for  each  cross  section 
of  the  member.  That  is  the  case  for  a  column  carrying  a  central  load  —  that  is, 
where  the  load  is  applied  to  the  centre  of  gravity  G  of  the  equivalent  section,  and 
consequently  M  =  o,  or  when  the  load  is  eccentric  and  M  =  Nx0.  This  is  the 
case  of  a  dam  where  the  curve  of  pressures  gives  N  and  x0  for  each  section. 

When,  however,  these  values  are  not  directly  furnished  by  statics,  the  procedure 
will  be  as  indicated  in  the  much  more  general  case  where  members  provide  a 
resistance  composed  simultaneously  of  compression  and  tension.  That  is  the  case 
which  really  justifies  the  employment  of  reinforcements. 

Article  11.  —  When  the  ordinary  principles  of  statics  furnish  the  normal  and 
tangential  components  of  the  external  forces  acting  on  each  cross  section  of  the 
member  considered,  and  also  the  bending  moment  at  that  section,  the  calculations 
necessary  for  the  design  of  a  reinforced  concrete  member  may  be  proceeded  with, 
without  any  reference  to  the  elastic  deformations  of  the  member. 

But  in  the  case  of  continuous  beams,  or  beams  wholly  or  partially  built  in  or 
arched  ribs  working  in  tension,  the  provisions  of  Article  1  1  are  applicable. 

The  Administration  are  prepared  to  accept  the  method  of  calculation  in  common 
use,  although  it  is  not  at  all  accurate.  It  consists  in  attributing  the  same 
coefficient  of  elasticity  in  tension  as  in  compression.  Once  this  hypothesis  is 
allowed  the  formulae  established  above,  under  the  restriction  that  there  is  only 
compression  on  any  cross  section,  become  general. 

Now,  by  virtue  of  the  intervention  of  the  equivalent  section  A,  these  formulae 
bring  back  the  resistance  of  a  reinforced  concrete  member,  that  is  to  say,  of  a 
heterogeneous  member,  to  that  of  the  resistance  of  an  equivalent  homogeneous  piece. 
All  the  general  and  classical  results  which  apply  in  the  case  of  the  latter  are  in 
consequence  capable  of  application  to  the  former.  Thus  to  determine  the  values 
of  N9  M  and  T  in  the  case  of  an  arch,  or  of  M  and  T  and  the  support  reactions  in 
the  case  of  a  straight  beam  loaded  transversely  (where  N  =  o),  it  suffices  to  adopt 
the  well-known  values  which  apply  to  homogeneous  members. 


12  REINFORCED    CONCRETE 

Thus  for  a  reinforced  concrete  beam  built  in  at  both  extremities,  the  greatest 
bending  moment  will  be  at  the  building  in,  and  will  have  for  its  value 

S     •      ;     .....  <"> 

The  bending  moment  at  the  middle  of  the  span,  of  sign  contrary  to  the  preceding, 
will  be  in  absolute  value 


For  partial  building  in  an  intermediate  value  between  the  latter  value  and  ~, 

the  value  of  the  bending  moment  in  a  simply  supported  beam  must  be  chosen. 

For  continuous  span  bridges  the  well-known  expressions  are  applicable  to 
reinforced  concrete  structures. 

In  the  case  of  a  double-hinged  arch  the  thrust  is  readily  obtained  from  tables  1 
relative  to  homogeneous  arches,  and  for  a  built-in  arch  the  tables  recently  published 
by  M.  Pigeaud  2  give  similar  information.  If  it  is  considered  that  there  is  only 
partial  constraint,  intermediate  values  between  those  furnished  by  the  tables  must 
be  chosen. 

Once  the  thrust  is  known,  all  the  necessary  data  to  determine  J/,  N  and  T 
graphically  or  by  calculation  are  obtained  for  each  of  the  sections  it  is  desired  to 
consider. 

A  more  correct  interpretation  of  the  regulation  is  obtained  by  taking  into 
account  the  actual  elastic  behaviour  of  concrete  in  tension.  As  a  result  of  different 
experiments  it  is  known  that  the  coefficient  of  elasticity  of  reinforced  concrete  in 
tension  only  conserves  a  value  sensibly  constant  up  to  a  limit  of  stress,  which  is  the 
same  as  the  limit  of  the  resistance  to  extension  of  a  similar  concrete  non-reinforced. 
Beyond  this  limit  the  concrete  becomes  in  effect  plastic,  that  is,  it  extends  without 
its  resistance  to  tension  being  modified,  owing  to  its  connection  with  the  reinforce- 
ments. There  is  no  difficulty  theoretically  in  building  up  on  this  hypothesis, 
together  with  that  of  Navier  relating  to  the  plane  deformation  of  plane  sections, 
expressions  for  the  resistance  of  materials,  but  the  expressions  become  much  more 
complex. 

By  one  or  other  of  the  above  methods  the  values  of  N,  J/and  T  will  be  found. 

From  these  the  unital  stresses,  at  least  on  the  more  highly  stressed  sections, 
must  be  determined.  In  this  latter  calculation  Article  1  1  prescribes  the  abstraction 
of  all  the  resistance  to  extension  of  the  concrete.  This  is  not  in  the  least  contra- 
dictory to  that  which  prescribes  the  taking  account  of  that  resistance  in  the 
calculations  of  deformation,  since  in  the  latter  the  abstraction  of  all  the  resistance 
to  extension  of  the  concrete  would  lead  to  excessive  values  being  put  on  the 
deformations  and  consequently  on  N,  M  and  T,  which  depend  on  the  calculated 
values  obtained  ;  on  the  other  hand,  the  local  stresses  must  be  determined  on  a 
hypothesis  representing  the  most  unfavourable  conditions  which  may  possibly 
supervene  in  practice.  In  fact,  the  concrete  cracks  more  or  less  from  the  tension 
side  of  each  member.  These  microscopic  cracks,  or  even  a  fissure  at  any  one  place, 
have  very  little  effect  on  the  deformation  of  the  member  as  a  whole,  although  the 
local  stress  in  the  reinforcement  at  the  fissure  will  be  materially  increased  owing 
to  the  complete  annulling  of  the  tension  resistance  of  the  concrete. 

1  Tables  de  Bresse,  published  by  Gauthier  Villars,  55,  Quai  des  Grands  Augustins,  Paris  (6e). 

2  "Annales  des  Fonts  et  Chaussees  "  (Deuxieme  trimestre  1905,  et  troisieme  trimestre  1906). 
Obtainable  from  H.  Dunod  and  E.  Pinat,  47,  Quai  des  Grands  Augustins,  Paris  (6e). 


CALCULATIONS   OF   RESISTANCE 


13 


Example  of  the  Application  of  the  above  Principles  to  a  Slab  of  T  Section 
and  to  a  Beam  of  Rectangular  Section, 

The  cross  section  of  the  member  dealt  with  is  shown  in  Fig.  2. 
If  there  are  no  compression  reinforcements  w  must  be  made  equal  to  zero.     In 
Fig.  3  the  ordinates  of  the  straight  line  A'B'  give  the  stresses  in  the  concrete,  and 


i b - JL 


F"" 

<; 
I 

* 


FIG.  2. 


the  appropriate  ordinates  multiplied  by  "  ra  "  give  the  values  of  the  stresses  in  the 
reinforcements. 


(a)  Simple  Bending. 

N  =  o,  the  algebraic  sum  of  the  elastic  forces  normal  to  the  cross  section  is 
consequently  zero.  From  this  equation  the  unknown  distance  yi  to  the  neutral 
axis  is  determined.  We  may  therefore  write 


o  =  -fi-  +  (b  —  b')  t  Ux  —  - j  +  m  w  (yi  —  d)  —  miv'  (h  —  d'  —  yi)     (16) l 

in  which  the  only  unknown  is  yi.     Also  the  angular  coefficient  K  is  determined 
thus : 

m  w'  (h—dr-  yi}  (h  —  d')     .          .          .          .     (17) 
where  K  is  the  only  unknown  value. 

These  formulae  implicitly  suppose  that  the  neutral  axis  falls  in  the  rib.     If  it 
falls  in  the  slab,  it  suffices  to  make  b'  =b  in  the  above  formulae,  which  become 


, 
o  =  --   + 


w 


=  -        +  m  w 


—  d)  —  m  w'  (h  —  d'  —  y±}     .          .          .  (18)  ! 

—  d)  d  —  m  10'  (h  —  d'  —  y^  (h  —  d')     .     (19) 


1  For  a  ribbed  slab  with  both  tension  and  compression  reinforcements  in  which  the  neutral 
axis  falls  in  the  rib  (see  expression  18a,  p.  14) — 


When  the  neutral  axis  falls  in  the  slab  or  for  a  member  of  rectangular  section  with  both 
tension  and  compression  reinforcements,  b  —  b'  and 

m(w  +  to')  )  2      2m{wd  +  w'(Ji  —  d'~)}  m(w  +  w')                         (i\ 

—J>          i    '                 ~^~  ~ ft7"" 

In  the  latter  case  when  there  is  only  tension  reinforcement  in  either  the  ribbed  slab  or 
member  of  rectangular  section,  w  =  o,  and 


//7/iM/\2      2//tM)'(/t  —  d')        mw' 

l~V\"F~j'f      ~~V~       ~~b~ 


14  REINFORCED    CONCRETE 

To  know  where  the  neutral  axis  falls,  and  in  consequence  whether  its  position 
is  determined  by  (16)  or  (18),  it  suffices  to  replace  yi  by  t  in  the  right-hand  member 
of  (18),  which  gives 

if  +  m  lv  (t  —  d)  —  m  iv'  (h  —  d'  —  t).  .          .  (18a) 

If  this  expression  has  a  positive  value,  the  neutral  axis  falls  in  the  slab  and  is 
determined  by  (18).  When  its  value  is  negative  the  neutral  axis  falls  in  the  rib 
and  is  determined  by  (16). 

Formulae  (18)  and  (19)  apply  also  to  a  rectangular  section  of  base  b  and  height  h. 

When  the  two  unknowns  (18)  and  (19)  are  determined,  the  maximum  values  of 
the  unital  stresses  are  : 


£'s  =  m  K  (h  —  d'  — 

(b)  Composite  Flexion  (or  Flexion  Combined  with  Thrust). 

In  addition  to  M  and  T,  as  in  the  previous  case,  JVis  also  known,  as  is  the  centre 
of  pressure  (7,  which  is  distant  c  from  the  compressed  face,  reckoned  positive  if  it 
falls  in  the  section  and  negative  if  it  lies  outside  the  latter.  In  the  following 
calculations  it  is  better  to  determine  in  the  first  place  the  position  of  the  neutral 
axis  by  its  distance  XC  (ya)  from  C  rather  than  by  ylf  its  distance  from  the 
compressed  face  (Fig.  3). 

Since  the  resultant  of  the  elastic  forces  coincides  with  TV",  the  sum  of  the  moments 
of  the  elastic  forces  relatively  to  C  is  zero,  which  gives  the  following  equation  to 
determine  %  :  — 


-  •  G  »  +  a  +  <>  -  *> 


d'  —  c)  =  o     (22) 
which  is  of  the  form 

y*  +  p  y*  +  q  =  o  .....    (23) 

where 


(24) 


The  term  in  y£  is  missing,  which  facilitates  the  solution  and  justifies  the  use  of  y2 
in  preference  to  y^, 

When  ^2  nas  been  found,  the  unknown  auxiliary  K  is  obtained  immediately  by 
the  equation 


TT    '  n  I 

-/!_  Zi 

-\-  m  w  [yz  +  c  —  d]  —  m  w'  [h  —  d'  —  c  —  y2]    .      (25) 
where  K  is  the  only  unknown. 

Formulas  (22)  to  (25)  inclusive  assume  that  the  neutral  axis  falls  in  the  rib.  If 
it  falls  in  the  slab,  as  also  in  the  case  of  a  beam  of  rectangular  section,  base  b, 
height  h,  it  suffices  to  make  bf  =  b,  which  gives 

_  _  3  C2  _  6  m  M;  ,    _  6  m  t^y        __        __ 


CALCULATIONS   OF   RESISTANCE 


15 


=  -  2  c3  - 


6  m  w 


(c  -  if  - 


(h  —  d'  —  c? 


(27) 


In  the  case  of  a  ribbed  slab,  to  know  if  the  neutral  axis  falls  in  the  rib  or  in  the 
slab  it  is  sufficient  to  determine  whether  or  not  the  first  member  of  the  equation 
(23)  has  or  has  not  contrary  signs  at  the  upper  and  lower  extremities  of  the  rib. 

When  the  unknowns  y2  an(i  K  are  determined,  there  is  obtained  from  the  former 

y\  =  y*  +  c 

for  the  distance  of  the  neutral  axis  to  the  compressed  face.  The  values  of  the 
unital  stresses  on  the  concrete  and  reinforcements  are  then  determined,  as  previously, 
by  formulae  (20)  and  (21). 

Remarks  on  the  Calculation  of  Slabs. 

When  a  floor  is  formed  of  a  slab  with  ribs  (Fig.  4),  a  rib  is  considered  with 
a  part  only  of  the  slab  c  c',  d  dr,  of  width  cd  =  b,  without  taking  into  account  the 
help  derived  from  the  neighbouring  parts. 

This  width  b  should  bear  a  relation  to  the  span  and  spacing  of  the  ribs  and 


|                        Roadway                                  \                               •*             \ 

Fillin                                                                                 "\ 

C 

1 

0                C 

I 

->K- 
I 

I        \ 

c 

-     L      - 

\ 



d' 

^\ 

Cross   Section. 

"T 

i 
! 
i 

1 

i 

i 
i 
i 

*1 

y 

*-  e  ---* 

Plan 

FIG.  4. 

the  thickness  of  the  slab.  It  should  never  exceed  one-third  of  the  span  s  of  the 
ribs,  nor  three-fourths  of  their  spacing  L. 

If  the  floor  has  to  support  concentrated  loads  between  the  ribs,  it  ought  to  be 
provided  with  two  series  of  reinforcements  at  right  angles.  There  is  generally 
given  to  the  feebler  reinforcement  a  total  section  per  metre  of  width  of  slab  at 
least  equal  to  one-half  of  the  stronger  section  per  metre  length  of  slab. 

To  calculate  the  thickness  t  of  the  slab,  an  isolated  load  might  be  replaced  by 
a  load  uniformly  distributed  on  a  rectangle  having  this  load  as  centre,  its  sides 
parallel  to  the  ribs  and  at  a  distance  apart  e  equal  to  the  sum  of  the  thicknesses  of 
the  slab  itself,  and  of  the  filling  and  of  the  pavement  which  it  carries,  its  sides, 

perpendicular  to  the  ribs,  having  for  spacing  e  +  •— .     The  load  thus  distributed 

o 

is  supposed  to  be  carried  by  a  band  of  the  floor  slab  of  width  e  -|-  —  and  of  span  L, 

u 

supported  on  two  consecutive  ribs. 


16 


REINFORCED   CONCRETE 


When  a  floor  is  supported  by  two  sets  of  ribs  at  right  angles,  spaced  at  spans 
L  and  L'  respectively,  the  bending  moment  in  the  span  L  may  be  obtained,  in  the 
absence  of  a  better  method,  by  calculating  it  as  if  the  ribs  spaced  L  apart  alone 
existed,  and  by  multiplying  the  figure  so  obtained  by  the  coefficient  of  reduction : 

1 


2 


r\i 


(L') 


The  bending  moment  in  the  span  L'  is  obtained  by  a  similar  process  and  by 
changing  the  letters  in  the  coefficient  of  reduction. 

Resistance  to  Slipping  of  Reinforcements  (Adhesion). 

If  it  has  been  found  that  in  two  neighbouring  sections  AB,  A'B'  of  a  member 
(Fig.   5),  spaced  As  apart,  there    are  unital   stresses  of  Rs'  and  ft",  the  .  total 

stresses  on  these  sections  will  be  w'Rs'  and  w'Its" 
respectively,  and  the  tendency  of  the  reinforcement 
to  slip  in  its  sheath  of  concrete  is  measured  by  the 
difference 


<- As --> 


w  - 


The  tendency  to  slip,  per  unit  of  surface  of  the 


reinforcement,    will    then    be 


w'  (JR.'  -  .£/') 


and 


P  .  As 

it  is  this  ratio  which  must  not  exceed  the  limit 
imposed  by  Article  6  of  the  instructions,  viz.,  one- 
tenth  of  the  maximum  compressive  stress,  or  O028 
of  the  crushing  strength  of  the  concrete  after  ninety 
days'  setting. 

When  stirrups  or  other  transverse  reinforcements 
are  attached  to  the  longitudinal  reinforcement  in 
such  a  manner  that  slipping  of  the  latter  cannot 
take  place  without  shearing  the  former,  then  the 
shearing  resistance  F  of  the  transverse  pieces 
occurring  on  the  length  As  of  the  longitudinal 
reinforcement  considered  as  the  product  of  the 
section  in  shear  by  the  allowable  shearing  stress  for  the  metal  ought  to  be  deducted 
from  the  slipping  force  wr  (fisf  —  R"\  It  is  then  sufficient  that  the  ratio 


FIG.  5. 


•w 


—  £"    —  F 


P.  As 

does  not  exceed  the  limit  allowed  for  adhesion. 

When  there  are  only  simple  ties  between  the  transverse  and  longitudinal  rein- 
forcements, these  are  not  sufficient  to  bring  the  shearing  strength  of  the  transverse 
pieces  into  action  as  a  reinforcement  lent  to  the  resistance  to  slipping  of  the 
longitudinals.  Consequently  no  account  ought  to  be  taken  of  the  shear  resistance 
of  the  transverse  reinforcements.  The  ties,  however,  serve  other  purposes  and 
ought  to  be  provided. 

Longitudinal  Slipping  of  the  Concrete  on  Itself  and  Shearing  Resistance. 

Consider  a  portion  of  the  member  lying  between  two  transverse  sections  AB 
and  A'B',  distant  apart  As,  and  having  a  longitudinal  reinforcement  a'b'  in  the 
tension  side  of  the  member.  Consider  a  horizontal  section  of  the  member  in  the 


CALCULATIONS   OF   RESISTANCE 


17 


stretched  part  of  the  concrete,  that  is,  between   the  reinforcement  and  the  neutral 
plane  and  parallel  to  the  latter.     Let  wc  be  the  area  of  this  section. 

As  the  tensions  in  the  concrete  normally  to  mB  and  nB'  are  not  taken  account 
of,  the  portion  m  n  BB'  of  the  member  is  in  equilibrium  under  the  influence  of  the 
tensions  w'R8'  and  w'R"  of  the  longitudinal  reinforcements  and  of  the  longitudinal 
shearing  stress  on  the  plane  mn.  The  value  of  this  longitudinal  shearing  stress 
per  unit  area  is 

w'  (R,>  -  R,«) 

wc 

and  ought  not  in  any  case  to  exceed   the  stress  allowed  for  the  shearing  of  the 
concrete. 

This  stress  (28)  remains  constant  up  to  the  neutral  plane.  Above  that  plane 
it  diminishes  by  the  effect  of  the  compression,  so  that  what  has  been  taken  account 
of  here  represents  the  maximum  stress. 

If  transverse  reinforcements  are  employed  to  resist  efficiently  the  longitudinal 
slipping,  they  might  be  taken  account  of  as  described  in  the  discussion  of  adhesion. 

The  vertical  shearing  stress  at  each  point  is  besides,  as  is  well  known,  the 
same  in  magnitude  as  the  longitudinal  slipping  force  just  considered. 

Buckling  of  Compressed  Pieces. 

Article  12. — To  ensure  that  buckling  of  compressed  pieces  will  not  occur,  the 
following  inequality,  which  expresses  Rankine's  formula,  must  be  satisfied  : 

+  fojsb)<*«  •     •     •     •  (^) 

The  varying  values  of  k  to  suit  the  different  end  conditions  met  with  in  practice 
are  as  follows  : — 

TABLE  No.  2. 


A1 


End  conditions. 


Kemarks. 


Built  in  at  one  end,  free  at  the  other 
Jointed  at  both  ends 
Jointed  at  one  end,  built  in  at  the 
other. 

Built  in  at  both  ends 


If  the  building  in  is  imperfect,  a  mean 
value  between  J  and  1  should  be 
chosen. 

If  the  building  in  at  one  end  is  im- 
perfect, a  mean  value  between  ^  and 
\  should  be  taken.  If  it  is  imperfect 
at  both  ends,  a  mean  value  between 
and  1  should  be  chosen. 


When  the  compression  member  is  of  great  length,  it  happens  that   unity  is 

k  I2 


negligible    in    comparison    with    the  number 


inequality  which 


expresses  the  condition  of  stability  might  be  simplified  thus  : 


•or 


A  '  1 0,000  r 
-10,000 


(30) 


R.C. 


18  REINFORCED   CONCRETE 

The  average  value  of  Rc  is  about  710  Ibs.  per  square  inch,  and  the  coefficient 
of  elasticity  of  concrete  about  on  the  average  one-tenth  that  of  steel,  that  is, 
Ec  =  2,844,000  Ibs.  per  square  inch. 

The  product  10,000  Rc  =  7,100,000  Ibs.  per  square  inch. 

2    ~p 

The  product  -  -  =  7,030,000  Ibs.  per  square  inch. 
These  are  sensibly  equal,  so  that  (30)  may  be  rewritten  : 


which  is  Euler's  formula  with  a  coefficient  of  security  of  4.  It  is  thus  seen  that 
the  indications  furnished  by  this  formula  agree  with  those  of  the  Rankine  formula 
for  very  long  pieces. 

If  in  addition  to  the  purely  compressive  stress  on  the  member  there  is  a  bending 
moment,  the  effect  of  which  cannot  be  considered  negligible,  e.g.,  the  case  of  an 
eccentrically  loaded  column,  or  of  a  long  column  exposed  to  wind  pressure,  the 
maximum  compressive  stress  due  to  this  bending  moment  must  be  introduced  into 
the  inequality  (29)  in  order  to  completely  state  the  conditions  of  stability. 

The  stress  due  to  this  bending  moment  is  expressed  by 

^c=^     ......     (31a) 

o^I  *<=^   ......     (314) 

Rankine's  formula  is  then  represented  by  one  or  the  other  of  the  following 
inequalities  :  — 


Execution  and  Tests  of  Works. 

The  Commission  point  out  that  comment  on  the  remaining  articles  of  the 
Instructions  is  superfluous.  They  limit  themselves  to  the  remark  regarding  the 
execution  of  works  that  in  reinforced  concrete  construction,  perfection  of  execution 
is  the  essential  condition  of  success.  Accidents  which  have  happened  are  in  general 
due  to  the  mediocre  quality  of  the  materials  used  or  their  improper  employment. 
It  is  necessary  to  exercise  a  special  supervision  over  the  production  and  the  purity 
of  the  materials  used,  their  mixture,  the  quality  and  the  quantity  of  the  water  used 
in  the  manufacture  of  the  concrete,  the  ramming  and  placing  of  the  concrete 
round  the  reinforcements,  and  the  stability  of  the  latter  till  the  enveloping 
concrete  is  properly  in  position. 


CHAPTER  III 

ANNEX  TO  THE  EXPLANATORY  CIRCULAR  BY  THE  FRENCH  MINISTRY  OF  PUBLIC 
WORKS,  BEING  A  REPORT  ON  THE  DRAFT  REGULATIONS  OF  THE  GOVERNMENT 
COMMISSION  BY  THE  COMMISSION  NOMINATED  BY  THE  GENERAL  COUNCIL  OF 
BRIDGES  AND  ROADS  (abridged). 

As  explained  in  the  Introductory  Note,  this  commission,  consisting  of  M.  Maurice 
Levy  as  President  and  Reporter,  and  MM.  de  Preaudeau  and  Vetillart,  reconsidered 
the  whole  question  of  the  draft  regulations  presented  to  the  Minister  of  Public 
Works  by  the  larger  Government  Commission,  and  as  a  result  of  their  labours  the 
regulations  took  the  form  which  appears  in  Chapter  I. 

They  suggested  the  substitution  of  the  word  "  Instructions "  for  the  word 
"Regulations,"  as  conveying  a  sense  of  less  permanence  and  finality  without  losing 
any  of  the  obligatory  character  of  the  latter. 

They  also  reconsidered  the  propriety  of  authorising  the  high  working  stress 
proposed  by  the  Government  Commission.  After  much  consideration  and  discussion, 
they  came  to  the  conclusion  that,  taking  into  account  the  methods  of  calculation  by 
which  the  stresses  would  be  arrived  at,  tjie  limits  defined  in  Articles  4  and  5 
would  be  safe  in  practice. 

The  fundamental  premise  of  all  calculations  in  reinforced  concrete  is  the  ratio 
expressing  the  equivalence  of  equal  sections  of  reinforcement  and  of  concrete  repre- 
sented by  the  symbol  "m."  The  Government  Commission  did  not  come  to  a 
unanimous  decision  on  the  value  of  m.  Two  members,  MM.  Rabut  and  Mesnager, 
were  of  opinion  that  this  number  should  be  taken  equal  to  10,  whilst  the  majority 
of  the  commission  decided  that  it  should  have  a  value  ranging  from  8  to  15.  The 
German  and  Swiss  regulations,  as  well  as  the  majority  of  French  and  Belgian 
writers,  adopt  the  value  15. 

Hypothetically  m  is  the  ratio  between  the  moduli  of  elasticity  of  the  reinforce- 
ment and  of  the  concrete.  From  the  experiments  of  M.  Mesnager,  which  agree 
closely  with  those  of  Professor  Bach  of  Stuttgart,  this  ratio  up  to  a  stress  of  850  Ibs. 
per  square  inch  on  a  concrete  composed  of  6  cwts.  Portland  cement  to  14*3  cubic 
feet  of  sand  to  2 8 '7  cubic  feet  of  gravel,  has  the  value  10.  With  the  value  15 
there  is  often  attributed  to  the  metal  a  greater  share  of  the  load  than  it  really  takes, 
so  that  the  concrete  is  more  highly  stressed  than  the  calculations  indicate.  Danger 
thus  arises  from  the  use  of  a  fixed  value  of  m. 

The  following  considerations  concerning  the  closely  interrelated  quantities,  "m," 
the  working  stress  and  the  coefficient  of  security,  lead  the  Commission  nominated  by 
the  General  Council  of  Bridges  and  Roads  to  agree  to  the  figures  appearing  in  the 
circular  accompanying  the  instructions. 

Consider  a  column  of  reinforced  concrete  in  which  the  calculated  stress  is  7 1 0  Ibs. 
per  square  inch.  A  test  cube  of  the  same  concrete  not  reinforced  broke  after 
ninety  days'  setting  under  a  load  of  2,840  Ibs.  per  square  inch.  The  column  would 

c  2 


20 


REINFORCED   CONCRETE 


9.Q4H 


7-09" 


0-276"  Dia.m 


then  be  said  to  have  a  coefficient  of  security  of  4.  This  is,  of  course,  only  a  con- 
ventional value.  The  real  value  of  the  coefficient  of  security  can  only  be  determined 
by  the  testing  to  destruction  of  the  actual  structure. 

This  actual  coefficient  of  security  was  determined  in  the  case  of  five  experimental 
columns  on  which  very  precise  rupture  experiments  were  carried  out  by  Professor 
Bach  of  Stuttgart.  The  breaking  loads  experimentally  determined  were  compared 
with  the  calculated  stresses  resulting 

1.  From  the  employment  of  the  working  stresses  allowed  by  foreign  regulations 

and  m  constant  and  equal  to  15. 

2.  From  the  employment  of  the 
working  stresses  allowed  by  the 
instructions,  taking  advantage  of  the 

/  P7  \ 

coefficient  of  increase    (  1  -f~  mr  -y    \ 

and  making  m  vary  from  8  to  15. 

The  columns  tested  had  the  cross 
section  shown  on  Fig.  6  and  a  length 
of  3 9 '3 7  inches.  The  area  of  each 
column  was  thus  96'9  square  inches. 
Each  was  reinforced  with  four  rods 
varying  from  0'59  to  1*18  inches  in 
diameter  and  spaced  at  7 '09-inch 
centres.  These  longitudinal  rods  were 
united  in  pairs  by  rods  of  0-276  inch 
diameter,  forming  double  transverse 
ligatures,  forming  the  four  sides  of 
a  square  and  spaced  longitudinally 
V,  the  volume  of  each  set  of  four 


FIG.  6. 


from  2  '46  inches  to  9  '8  4  inches  apart. 
ligatures,  was  3  '8  3  cubic  inches. 

Table  No.  3  is  a  resume  of  the  five  series  of  experiments. 


TABLE  No.  3. 


1. 

2. 

3. 

4. 

5. 

No.  of 
Experiment. 

Diameter  of 
Longitudinal 
Keinforcements. 

Spacing  of 
Transverse 
Reinforcements. 

Mean  Value  of  the 
Breaking  Load. 

Total  Cross 
Section  of  the 
Longitudinal 
Reinforcements. 

1 

Inches. 
0-59 

Inches. 
9-84 

Lbs.  per  square  inch. 
2,390 

Square  Inches. 

MO 

2 

0-59 

4-92 

2,520 

MO 

3 

0-59 

2-46 

2,915 

MO 

4 

0-79 

9-84 

2,420 

1-95 

5 

1:18 

9-84 

2,700 

4-39 

The  breaking  stress  of  a  non-reinforced  concrete  column  was  found  to  be 
2,020  Ibs.  per  square  inch  and  that  of  a  cube  of  this  concrete  2,500  Ibs.  per 
square  inch. 


21 


Supposing  m—  15  and  taking  Rc  =  500  Ibs.  per  square  inch,  which  would 
conform  to  the  German  regulations, 

N  =  500  (96-90  +  15  w). 

TABLE  No.  4. 


No.  of 
Experi- 
ment. 

15  w. 

(96-90  +  15  to). 

N. 

N 
96-9' 

Breaking 
Loads. 

Effective 
Co-efficient 
of  Security. 

Lbs.  per 

Lbs.  per 

(Inches).2 

(Inches.)2 

Lbs. 

inch.2 

inch.2 

1 

16-4 

113-3 

56,400 

582 

2,390 

4-1 

2 

16-4 

113-3 

56,400 

582 

2,520 

4-3 

3 

16-4 

113-3 

56,400 

582 

2,915 

5-0 

4 

29-3 

126-2 

62,800 

648 

2,420 

3-5 

5 

65-7 

162-6 

81,000 

834 

2,700 

3-2 

It  is  seen  that  the  effective  coefficient  of  security  is  a  very  variable  quantity. 
It  varies  between  5  and  3  '2,  which  indicates  that  the  hypothesis  of  m  =  15 
might  lead  to  serious  miscalculations. 

Now  in  terms  of  Article  4  of  the  instructions,  allowing  a  stress  of  710  Ibs. 
per  square  inch  instead  of  500  Ibs.  per  square  inch,  as  in  the  above  calculations, 
and  in  virtue  of  Article  5  we  increase  this  stress  according  to  the  coefficient  of 


ncrease 


which  leads  to 


'  V 
1  +  m 


Rc  =  710 


V' 

+  m' 


The  safe  working  loads  N   for  the  various  columns  are  given  by    the    formula 

N  =  JK0(96-9  +  m  .  w). 

The  values  of  mf  and  m    indicated  in  the    circular  are  adopted  and    are  given 
in   Table  No.   5. 

TABLE  No.  5. 


1. 

2. 

3. 

4. 

5. 

6. 

7. 

8. 

9. 

10. 

11. 

Nos. 

m. 

m  w. 

96-90  +  mw. 

Spacing  of 
Transverse 
Reinforce- 

m'. 

V 

y  ' 

K'  =    y, 

710  (l  +  m'  y\ 

N. 

N 
96-9' 

Effective 
Coefficient 
of 

ments. 

Security. 

Lbs.  per 

(Inches.  )2 

(Inches.)2 

(Inches). 

Lbs. 

inch.2 

1 

10 

11-01 

107-91 

9-84 

8 

0-00401 

734 

79,200 

818 

2-9 

2 

12 

13-18 

110-08 

4-92 

12 

0-00802 

779 

85,800 

886 

2-8 

3 

15 

16-43 

113-33 

2-46 

15 

0-01604 

882 

121,800 

1,258 

2-8 

4 

9 

17-52 

114-42 

9-84 

8 

0-00401 

734 

105,900 

1,094 

2-8 

5 

8 

35-03 

131-93 

9-84 

8 

0-00400 

734 

96,850 

1,000 

2-7 

The  figures    in    column   11     display  a    remarkable    constancy  and    admit  of 
fidence  in  the  values  of   "m"  and  "mf" 
also  justify  the  use  of  the  high- working  stress. 


confidence  in  the  values  of   "m"  and  "  m' '"  set  forth   in  the  Instructions,  and 


CHAPTER    IV 

SHORT  DESCRIPTION,  WITH  RESUME  OP  THE  RESULTS,  OF  THE  EXPERIMENTS  CARRIED 
OUT  AT  THE  LABORATORY  OF  THE  NATIONAL  SCHOOL  OF  BRIDGES  AND  ROADS 
UNDER  THE  PROGRAMME  OF  THE  SECOND  SUB-COMMITTEE. 

1.  Measurement  of  Contraction  during  Setting. 

To  measure  the  contraction  during  the  setting  of  cement  concrete,  four 
prisms,  each  3 '2 8  feet  long  and  of  approximately  6 -inch  side,  were  moulded 
vertically,  two  reinforced  and  two  without  reinforcement.  One  of  the  non-rein- 
forced prisms  was  kept  in  the  Court  of  the  Laboratory  covered  with  sacks  and 
watered  from  time  to  time,  the  others  were  kept  dry  on  supports  in  a  closed  shed. 

The  results  are  discussed  in  Chapter  V.,  p.   70. 

2.  Measurement  of  Elasticity  of  Concrete  without  Reinforcement. 

Two  prisms  of  concrete,  containing  6  cwts.  Portland  cement,  28*7  cubic  feet 
of  gravel  and  14'4  cubic  feet  of  sand  mixed  to  a  plastic  consistency,  each  3*28  feet 
long  and  of  square  section  of  1'64  feet  side,  were  subjected  to  compression  in  a 
hydraulic  press  after  setting  for  about  10^  months. 

Table  No.   6  gives  the  results  obtained. 


TABLE  No.  6. 


Compressive  Stress. 

Modulus  of  Elasticity. 

Load  Applied  Normal  to  Planes 
of  Ramming. 

Load  Applied  Parallel  to  Planes 
of  Hamming. 

Lbs.  per  square  inch. 

From  64  to  580 
From  64  to  970 
From  64  to  1,360 

Lbs.  per 
square  inch. 
4-20  x  106 
4-01   x  10« 
3-87  x  106 

Tons  per 
square  inch. 
1,875 
1,790 
1,728 

Lbs.  per 
square  inch. 
3-83  x  106 
3-77  x  106 
3-60  x  106 

Tons  per 
square  inch. 

1,710 
1,683 
1,608 

3.  Determination  of  the  Resistance  to  Crushing  of  Cement  Concrete 
prepared  in  Different  Degrees  of  Plasticity. 

Three  prisms  each  7'87  inches  square  and  19'68  inches  long  were  cast  verti- 
cally in  moulds,  the  concrete  consisting  of  12  cwts.  of  Portland  cement  to  28'7 
cubic  feet  of  gravel  and  14 -4  cubic  feet  of  sand. 


DETERMINATION   OF   SETTING   STRESSES 


23 


Prism  No.  1. — The  concrete  was  mixed  with  11 '6  per  cent,  of  water  by  weight 
of  dry  mixture  and  was  sufficiently  wet  to  pour  into  the  mould,  which  was 
completely  filled  in  that  way. 

1  Prism  No.  2. — The  mould  was  filled  for  three-quarters  of  its  height  with 
material  similar  to  that  in  Prism  No.  1 ;  the  remainder  of  the  mould  was  filled  with 
successive  layers  of  dry  mixture  strongly  rammed. 

Prism  No.   3. — The  mould  was  filled  with  ordinary  plastic  concrete  rammed. 

The  tests  in  each  case  were  made  fifty-four  days  after  moulding. 

TABLE  No.  7. 


Cross 

— 

Sectional 
Area  of 
Prisms  in 

Weight  in  Lbs.  per  cubic  foot  of  Concrete 
of  Prisms. 

Resistance 
to  Rupture 
by  Crushing. 

square  inches. 

Lbs.  per 

After  7  days. 

After  26  days. 

After  54  days. 

square  inch. 

Prism  No.  1 

63-24 

140-8 

138-4 

137-7 

2,092 

Prism  No.  2 

63-23 

143-2 

142-2 

141-8 

>  2,510  2 

Prism  No.  3 

62-46 

141-6 

140-0 

139-5 

2,440 

4.  Influence  of  the  Percentage  of  Keinforcement  on  the  Stresses 
developed  during  Setting.8 

Nine  pairs  of  cylinders  were  manufactured,  each  19 '7  inches  long  and  3 -9 
inches  in  diameter,  each  pair  containing  a  similar  reinforcing  rod,  the  area  of  which 
varied  throughout  the  series  from  a  percentage  of  0-23  to  9'0.  One  cylinder 
of  each  pair  consisted  of  6  cwts.  of  Portland  cement,  2 8 -7  cubic  feet  of  gravel 
and  14*4  cubic  feet  of  sand,  the  other  of  10  cwts.  of  Portland  cement  to  the  same 
quantities  of  sand  and  gravel.  The  cylinders  of  the  former  mixture  were  kept 
in  air,  those  of  the  latter  in  water. 

No  very  definite  results  were  obtained ;  but  at  the  end  of  seven  months  it 
was  found  that  the  shortening  of  the  reinforcements  of  the  test  cylinders  kept 
in  air  was  0-018  per  cent,  when  the  percentage  reinforcement  was  0'23, 
and  O'OIO  per  cent,  when  the  percentage  reinforcement  was  9.  The 
corresponding  percentage  elongations  of  the  reinforcements  of  the  cylinders  kept 
in  water  were  O'OIO  per  cent,  and  0*009  per  cent,  when  the  percentage  rein- 
forcements were  0*23  and  9-0  respectively. 

The  shortenings  and  elongations  were  measured  on  a  length  of  1*64  feet. 

5.  Tension  Tests.4 

Four  prisms  of  square  section  3 -94-inch  sides  and  78*8  inches  long,  rein- 
forced with  four  round  rods,  each  0*24  inch  diameter,  giving  a  percentage  reinforce- 
ment of  1'13,  were  made  of  concrete  consisting  of  6  cwts.  of  Portland  cement, 
28*7  cubic  feet  of  gravel  and  14-4  cubic  feet  of  sand,  and  gauged  with  8-8  percent, 
of  water  by  weight  of  dry  mixture. 

1  See  note  on  p.  74. 

3  This  stress  only  produced  fissures  without  leading  to  total  rupture. 
8  For  notes  on  these  tests  by  M.  Considere,  see  pp.  105,  106. 

4  For  notes  on  these  tests  by  M.  Considere,  see  Chapter  VII.,  1. 


24 


REINFORCED   CONCRETE 


Prism  No.  1  was  tested  by  a  gradually  increasing  load  until  cracking  was 
observed.  Under  a  load  of  550  Ibs.  per  square  inch,  when  the  elongation 
reached  0*135  per  cent,  of  the  original  length  (measured  on  one  metre),  fissures 
were  observed. 

Prism  No.  2  was  tested  by  repeatedly  removing  the  load  and 
reapplying  it.  Twenty-five  repetitions  were  made.  The  last  load  applied  was 
293  Ibs.  per  square  inch,  which  produced  an  elongation  of  O'OGl  per  cent,  of 
the  original  length  without  producing  any  visible  cracks.  The  permanent 
deformation  under  this  load  was  0'0265  per  cent,  of  the  original  length. 

The  reinforcing  rods  were  carefully  cut  out  and  the  concrete  of  the  prism 
subjected  to  bending  tests.  The  breaking  load  in  the  first  of  these  bending 
tests  corresponded  to  a  tension  of  133  Ibs.  per  square  inch,  and  in  the  second 
to  a  tension  of  126  Ibs.  per  square  inch. 

Prism  No.  3. — This  prism  was  tested  similarly  to  No.  2.  After  the  tenth 
loading  the  permanent  deformation  found  on  unloading  was  observed  not  to 

increase,  and  after  the  twentieth 
loading  the  load  was  allowed  to 
remain  on  for  fifteen  hours.  No 
appreciable  increase  in  the  exten- 
sion took  place.  The  load  applied 
in  each  case  was  255  Ibs.  per  square 
inch,  and  the  extension  due  to  the 
twenty-fifth  application  was  0'0165 
per  cent,  of  the  original  length. 
The  total  extension  from  the  com- 
mencement of  the  experiment  was 

["*_""  ~ — I     0*0435    per   cent,    of    the    original 

length  without  any  appearance  of 
fissures. 

Prism  No.  4. — This  prism  was 
tested  as  was  Prism  No.  1  by  a 
gradually  increasing  load.  When 
the  load  had  reached  540  Ibs.  per 
square  inch  and  the  elongation 
0'13  per  cent,  of  the  original 
length,  fissures  appeared  uniformly 
over  the  whole  length  of  the 

prism    at    intervals    of    from    3    to 
FIG.  7.  £   .     , 

b   inches. 

From  a  portion  of  the  concrete  of  Prism  No.  1  which  had  been  loaded  to 
550  Ibs.  per  square  inch,  the  coefficient  of  elasticity  of  concrete  in  compression 
was  determined  and  the  following  values  were  obtained  :— 

For  stresses  between 

70  and  700  Ibs.  per  square  inch,  2'105  X  106lbs.  per  inch2  or  940  tons  per  inch.2 
700  and  1,140  Ibs.  per  square  inch,  2 '180  X  106  Ibs.  per  inch2  or  973  tons  per  inch.2 

70  and  1,140  Ibs.  per  square  inch,  2'130  X  106  Ibs.  per  inch2  or  951  tons  per  inch.2 

The  steel  wire  used  in  the  manufacture  of  the  prisms  had  an  apparent  limit 

of  elasticity  of  19-8  tons  per   square  inch,   a  breaking  strength  of   27   tons  per 

square    inch,  with    an    elongation    of     20'5    per    cent,    on    7 '87  inches,    and    a 

modulus  of  elasticity  of  13,000  tons  per  square  inch. 


K  8'  * 

<--4'-f-  ->J 

t^-Line  of  Fracture 
of  Concrete 

L/ne  of  Fracture     / 
of  Concrete  ' 

*^Art/F,cia/  Shear  Plane 

o-               ' 
*-•"'  -•  o  >• 

TESTS   OF   SHEAR   RESISTANCE 


25 


6.  Shearing  Tests. 

Six  rectangular  prisms,  each  11*8  inches  X  11 '8  inches  X  23*6  inches  long,  were 
made  in  three  series,  each  consisting  of  concrete  containing  6  cwts.  of  Portland 
cement,  28 '7  cubic  feet  of  gravel  and  14'4  cubic  feet  of  sand. 

The  prisms  were  moulded  in  wooden  boxes  in  two  halves,  with  the  reinforce- 
ments vertical.  As  soon  as  the  first  half  of  each  prism  was  set  it  was  turned  in  the 
mould  and  the  other  half  formed,  a  sheet  of  oiled  paper  being  placed  between  the 
halves  to  secure  a  division  plane. 

Fig.  7  shows  the  prism  with  division  plane  and  the  method  of  applying  the 
shear,  and  Table  No.  8  gives  a  resume  of  the  results  obtained. 

The  planes  along  which  fissuring  took  place  are  indicated  by  dotted  lines  on  the 
diagram. 

1st  series  of  prisms  were  reinforced  with  six  sheet-iron  straps  1-575  inches 
X  0-084  inch,  giving  a  percentage  reinforcement  of  the  cross  section  of  0-57. 

2nd  series  of  prisms  were  reinforced  with  two  round  rods  each  0'716  inch 
diameter,  giving  a  percentage  reinforcement  of  0'58. 

3rd  series  of  prisms  were  reinforced  with  six  rods  of  0*394  inch  diameter, 
giving  a  percentage  reinforcement  of  0'52. 

TABLE  No.  8. 


Shearing  Effort  Applied  to 
the  Division  Plane. 


Total  Stress. 


Lbs. 


Unital  Stress 
per  square 

inch  of 
Reinforce- 
ment. 
Tons. 


Mean  Relative 

Displacement 

of  the  two 

halves. 


Inches. 


Remarks. 


29,730     |      16-57 


809 

6,590 

13,550 

14,690 

20,700 


0-45 
3-68 
7-56 
8-13 
11-53 


SERIES  I. — 1st  Prism. 
0-50         |  Maximum  load  attained. 
'2nd  Prism. 


7,750 

4-32 

— 

Stress   beyond    which    a    movement 

imper- 

ceptible  to  the  eye  was  indicated. 

18,640 

10-41 

— 

Relative  displacement  became  visible. 

25,600 

14-29 

— 

Sudden  displacement. 

28,600 

14-94 

0-50 

Maximum  load.     Concrete  fissured. 

SERIES  II. — 1*2  Prism. 


0-0005 
0-0044 
0-0163 
0-0263 
0-70 


Prism  fissured. 


26 


REINFORCED   CONCRETE 


TABLE  No.   8 — (continued). 


Mean  Eelative 

Shearing  Effort  Applied  to 
the  Division  Plane. 

Displacement 
of  the  two 

halves. 

Unital  Stress 

Remarks. 

per  square 

Total  Stress. 

inch  of 

Reinforce- 

ment. 

Lbs. 

Tons. 

Inches. 

SERIES  II. — 2nd  Prism. 


6,590 

18,850 
23,280 

3-68 

10-42 
12-89 

0-36 

Stress   beyond   which    a    movement    imper- 
ceptible to  the  eye  was  indicated. 
Visible  displacement  took  place. 
Concrete  fissured. 

SERIES  III.  —  1st  Prism. 

13,550 
25,300 

8-27 
15-50 

0-33 

Relative  displacement  became  visible. 
Concrete  fissured. 

2nd  Prism. 

17,020 
24,870 

10-43 
15-27 

0-43 

Relative  displacement  became  visible. 
Concrete  fissured. 

The  steel  reinforcing  the  prisms  used  in  the  shearing  tests  had  the  properties 
indicated  by  the  following  figures  : — 


TABLE  No.   9. 


Practical 
Elastic  Limit. 

Breaking  Load 
on  Original 
Section. 

Elongation 
per  cent,  on 
8  inches. 

Modulus  of 
Elasticity. 

Sheet  steel,  1-57  inches 
X  0-084  inch. 

Tons  per  inch.2 
20-7 

Tons  per  inch.2 
27-5 

21-5 

Tons  per  inch.3 

13,000 

Round  rod,  0-394  jnch 
diameter. 

18-8 

26-5 

25-7 

15,500 

Round  rod,  0-717  inch 
diameter. 

15-8 

24-0 

33 

14,800 

TESTS   OF   SHEAR   RESISTANCE 


27 


7.  Torsion  Tests. 

Two  cylinders,  each  39'37  inches  long  and  4*21  inches  diameter,  were  reinforced 
longitudinally  by  four  steel  wires  placed  symmetrically  in  the  section  about  0*47  inch 
from  the  surface.  The  concrete  was  of  the  same  proportions  as  that  described  on 
p.  25.  The  moulds  were  placed  vertically  and  filled  in  three  parts,  one 
immediately  after  the  other. 

As  soon  as  the  cylinders  were  removed  from  the  moulds,  square  heads  for  the 
purpose  of  applying  the  torsion  were  moulded  on  each  extremity. 

In  the  application  of  the  test  the  cylinders  were  kept  horizontal  and  the  torsion 
applied  by  means  of  a  lever.  The  variations  in  length  of  the  cylinders  during  the 
test  were  measured  on  one  of  the  reinforcing  rods,  the  ends  of  which  projected 
beyond  the  concrete. 

The  results  obtained  were  the  following  : — 


TABLE  No.   10. 


Moment  of 
Torsion. 

Foot-lbs. 

Total  Elongations 
per  cent,  of 
Original  Length. 
Measured  on 
39-37  inches. 

Remarks. 

36 

108 
253 
290 


36 
108 
253 
325 
360 


1.   Cylinder  with  Reinforcements  0-213  inch  diameter. 


0-0 
0-002 
0-010 
0-013 


Rupture   took  place  when  torsion  was  increased 
beyond  this  value. 


Cylinder  with  Reinforcements  0'300  inch  diameter. 


0-0 

0-001 

0-005 

0-010 

0-016 


A  crack  appeared  at  this  load. 
Rupture  took  place  immediately  after  this  torque 
was  applied. 


The  direction  of  the  principal  fissures  with  the  generator  of  the  cylinder  was  61° 
for  the  first  cylinder  and  45°  for  the  second. 

8.  Resistance  to  Slipping  of  Reinforcements. 

1.  Four  test  pieces,  consisting  of  mild  steel  cylinders  4*18  inches  diameter, 
rough  from  the  rolls,  were  enveloped  for  a  length  7*87  inches  in  a  square  block  of 
concrete  of  1 2 "20-inch  side,  otherwise  not  reinforced.  The  composition  of  the  concrete 
was  6  cwts.  Portland  cement  28*7  cubic  feet  gravel,  14*4  cubic  feet  sand,  and  it  was 
filled  into  the  mould  by  ramming. 

In  the  case  of  two  of  the  test  pieces  tension  was  applied  to  the  steel  cylinder 
and  in  the  other  two  a  thrust  was  applied. 


28 


REINFORCED   CONCRETE 


The  age  of  the  concrete  at  the  time  of  the  test  was  seventy-two  days,  and  failure 
took  place  by  the  splitting  of  the  concrete  block,  in  the  case  of  the  first  test  piece, 
when  a  load  was  applied  corresponding  to  a  stress  of  97  Ibs.  per  square  inch  of  area  of 
contact  of  the  metal  and  concrete.  In  the  case  of  the  second,  failure  took  place  at 
190  Ibs.  per  square  inch,  and  in  the  case  of  the  third  and  fourth  test  pieces  to  which 
a  thrust  was  applied  at  stresses  of  215  Ibs.  per  square  inch  and  235  Ibs.  per 
square  inch  respectively.  The  low  stress  obtained  in  the  first  case  is  accounted  for 
by  a  defect  in  the  testing  apparatus. 

2.  Four  test  pieces  similar  in  all  respects  to  the  above,  but  having  the  concrete 
surrounding  the  steel  cylinder  reinforced  with  two  rings  of  sheet  steel  1'18  inches  X 

0*23  inch,  and  with  three  longitudinal 
wires  0'98  inch  diameter,  were  similarly 
tested.  After  six  months'  setting  slip- 
ping took  place  when  stresses  of  347 
and  360  Ibs.  per  square  inch  of  area  of 
contact  between  the  concrete  and  the 
steel  had  been  applied  by  tension  and 
when  stresses  of  356  and  464  Ibs.  per 


!    :  i 

-I-4-- 


075'tol" 


FIG.  8. 


square  inch  had  been  applied  by 
thrust.  In  each  case  no  cracking  of  the 
enveloping  cylinder  of  concrete  occurred 
when  the  first  slipping  of  the  cylinder 
through  its  concrete  envelope  took  place, 
which  slipping  amounted  to  about 
0*08  inch.  The  cylinder  was  able  after 

this  initial  slipping  had  occurred  to  resist  a  stress  tending  to  cause  further 
slipping  amounting  on  the  average  over  the  four  specimens  to  303  Ibs.  per 
square  inch. 

3.  Test  pieces  representing  parts  of  beams  and  formed  as  indicated  in  Fig.  8 
were  prepared.     They  were  divided  into  three  series  according  to   the  proportions 
of  cement  employed  in  the  concrete  : — 

Series      I.     3  cwts.  cement,  28*7  cubic  feet  gravel,  and   14'4  cubic  feet  sand. 
Series    II.     6       „          „        28'7  „  „  14'4 

Series  III.  10       „          „        28'7  „  „  14'4 

They  were  tested  by  tension  applied  to  the  projecting  end  of  the  reinforcement. 

The  test  pieces  were  non-reinforced  as  at  "a,"  reinforced  with  ordinary 
(Hennebique)  stirrups  as  at  "6"  or  reinforced  with  open  stirrups  as  at  "c." 

The  results  obtained  are  given  in  Table  No.  11,  p.  29. 

In  the  case  of  the  test  pieces  without  stirrups  a  crack  occurred  in  each  case 
along  the  middle  of  the  lower  face  following  the  reinforcing  bar  at  the  moment  of 
slipping.  In  none  of  the  others  were  fissures  observed. 

4.  Additional  Tests  on  the  Slipping  of  Reinforcements  in  Concrete  made  ivith 
French    Quick-setting    Cements. — Six    test    pieces    were    made    of    the    form    and 
dimensions  shown  in  Fig.  8,  of  type  "  a,"  without  transverse  reinforcements  of  any 
kind.      The  concrete  in  each  case  was  of  the  proportions  of  Series  II. 

With  a  cement  setting  of  which  commenced  in  nine  minutes  and  was  complete 
in  thirteen  minutes,  the  average  resistance  to  slipping  per  square  inch  of  the  surface 
of  contact  of  reinforcement  and  concrete  was  60  Ibs.  per  square  inch  after  twenty- 
four  hours,  and  232  Ibs.  per  square  inch  after  twenty-eight  days. 

With  a  cement  which  commenced  setting  in  air  in  one  hour  and  was  set  in  two 


TESTS   OF   RESISTANCE   TO   SLIPPING 


29 


hours,  the  resistance  was  31  Ibs.  per  square  inch  after  twenty-four  hours  and  91  Ibs. 
per  square  inch  after  twenty-eight  days. 

5.  Tests  were    made  of    the  resistance  to   slipping   of  the    wires   in  an    old 
reinforced  concrete  sleeper.     The  diameter  of  the  wires  was  0*197  inch. 

TABLE  No.   11. 


Average  Stress 

_ 

Stress  which 
produced  the 
First  Slipping 

Maximum 
Stress  under 
which  Slipping 
ceases  after 

under  which 
the  Reinforce- 
ment leaves 
its  Bed,  when 

Age  of  Test 
Piece. 

Reinforcement. 

the  First 
Slipping. 

the  Displace- 
ment reaches 

0-2  inch. 

Lbs.  per 
square  inch. 

Lbs.  per 
square  inch. 

Lbs.  per 
square  inch. 

Months. 

(a)  Without  stirrups  . 

(b)  With  ordinary  stirrups 

(c)  With  open  stirrups 


(a)  Without  stirrups 


SERIES  I. 

317 

102 

60 

3 

267 

236 

182 

3 

304 

182 

142 

3 

SERIES  II. 


(6)    With  ordinary  stirrups  . 


(c)   With  open  stirrups 


400 

155 

115 

422 

161 

141 

230 

158 

119 

102  . 

91 

115 

283 

232 

202 

411 

311 

284 

300 

245 

200 

404 

300 

272 

284 

245 

245 

240 

215 

182 

305 

262 

226 

472 

353 

312 

556 

357 

313 

365 

298 

259 

424 

383 

302 

SERIES  III. 


(a)  Without  stirrups  . 

433 

146 

148 

3 

(6)    With  ordinary  stirrups  . 

579 

483 

417 

o 

(c)    With  open  stirrups 

454 

375 

326 

3 

Longitudinally  the  wires  were  not  straight,  but  presented  considerable  undula- 
tions. Slipping  of  the  reinforcement  took  place  generally  about  1,150  Ibs.  per 
square  inch  of  the  surface  of  contact,  although  in  one  case  slipping  took  place  at 


30 


REINFORCED   CONCRETE 


820  Ibs,  per  square  inch.  In  three  cases  the  wire  broke  outside  the  concrete 
before  slipping  had  taken  place  when  the  stress  had  reached  1,050,  1,310  and  590  Ibs. 
per  square  inch  respectively  of  the  surface  of  contact  between  the  wire  and  the 
concrete. 

9.  Bending  of  Beams. 

Twenty-three  specially  manufactured  beams  were  tested,  and  a  resume  of  the 
results  obtained  is  given  in  Table  No.  12,  pp.  32-38. 

Fig.  9  shows  in  outline  the  method  of  applying  the  test  loads  to  the  beams 
A  to  G  inclusive.  By  this  arrangement  there  is  obtained  a  uniform  bending 
moment  between  the  points  of  application  of  the  load,  and  a  uniform  shear  between 
the  latter  and  the  points  of  support  of  the  beam. 

The  sand  and  gravel  used  were  carefully  measured  by  weight,  allowance  being 
made  for  moisture  in  the  sand  and  for  sand  and  moisture  in  the  gravel.  When 


T— 

• 


aratuses   for  Measuring  Strajns 


« 3  28' -4 

< —  6-23' i 


3-28  H 

G  23' 


FIG,  9. 

beam  A  was  prepared  the  sand  contained  4  per  cent,  of  its  weight  of  water  and  the 
gravel  2*7  per  cent.  The  results  of  this  method,  however,  were  sensibly  the  same 
as  those  obtained  by  the  volumetric  methods  used  in  practice. 

The  granulometric  composition  of  the  materials  used  was  as  follows  : — 

Sand. 

Weight  per  cubic  foot  =  9  9 '7  Ibs. 
Granulometric  composition,  weights  per  cent. 
0*197     inches  diameter  to  0'079     inches  diameter 
0-079  „  „          0-0197       „  . 

0-0197  0-0 


Gravel. 

Weight  per  cubic  foot  =  9  3 '4  Ibs. 
Granulometric  composition,  weights  per  cent. 
0*984  inches  diameter  to  0*787  inches  diameter  . 
0*787        „  „         0*394       „  . 

0*394  0*197 


100 


3-5 
71*7 

24-8 

100 


For  the  tests  of  beams  J  to  U  inclusive  an  alteration  in  the  spacing  of  the  points 
of  support  and  of  application  of  the  loads  was  made,  giving  the  ends  of  the  beam  a 


TESTS  OF   BEAMS 


31 


greater  overhang.  The  effect  of  the  projection  of  reinforcements  beyond  the  points 
of  support  can  thus  be  studied.  The  arrangement  is  outlined  in  Fig.  10. 

In  beam  H,  the  whole  load  was  applied  as  a  concentrated  load  midway  between 
the  points  of  support,  whilst  in  beams  /,  V  and  W  the  points  of  application  of  the 
load,  were  3' 2 8  feet  apart. 

Manet-Rabut  apparatuses  for  measuring  strains  were  fixed  to  the  beams  in  the 
positions  indicated  in  Figs.  9  and  10  by  rods  built  into  the  concrete.  The  strains 
in  the  reinforcements  were  measured  by  similar  apparatuses  fixed  directly  to  the 
latter,  which  were  exposed  for  a  short  length  by  careful  chiselling. 

The  relative  slipping  of  the  concrete  and  the  reinforcement  was  obtained  in 
either  of  three  ways  : — 

1.  By  the  use  of  an  apparatus  fixed   to   the  concrete  at  the  end  of  the  beam, 
operated  by  a  rod  from  the  end  of  the  reinforcement,  bared  for  the  purpose. 

2.  By  means  of  an  apparatus  fixed  to  the  concrete,  and  measuring  the  relative 
movement  of  the  reinforcement  in  a  vertical  plane  normal  to  the  beam  1J  inches 
distant. 

3.  By  means  of  a  microscope  fixed  to  the  concrete,  and  reading  on  a  reference 
mark  on  the  reinforcement  in  the  plane  of  the  microscope. 

The  deflections  were  measured  by  means  of    a    Rabut    recording  apparatus 


•.Apparatuses  for  Measuring  /\ 
......  Strain" 


J 


FIG.  10. 

fixed  to  each  face  of  the  beam  midway  between  the  tie  rods,  whilst  the  extension 
of  the  latter  and  the  deflections  of  the  loading  system  were  also  recorded,  so  that 
the  actual  values  of  the  deflections  of  the  beam  were  obtained. 

All  the  beams  had  a  length  over-all  of  13' 12  feet,  with  the  exception  of  beams  U 
and  F,  which  had  an  over-all  length  of  9*84  feet. 

The  ends  of  the  longitudinal  reinforcements  of  beams  A,  B,  C,  D,  F  and  G 
were  fish-tailed  according  to  the  Hennebique  practice,  whilst  in  beam  E  they  pro- 
jected 2  inches  at  each  end  for  measurement  purposes.  In  beams  H  to  ^inclusive, 
with  the  exception  of  /,  the  longitudinal  reinforcements  were  cut  to  a  uniform 
length,  \\  inches  shorter  than  the  beam,  and  left  simply  with  square-cut  ends,  whilst 
in  beams  7,  U,  V  and  W  each  end  of  the  longitudinal  reinforcements  was  returned 
square  upwards  for  a  length  of  2J  inches. 

Beams  A  to  G  inclusive  had  measuring  apparatuses  attached  to  the  vertical 
faces  of  the  beams  near  the  upper  and  lower  faces  and  also  at  the  neutral  axis  for 
the  purpose  of  verifying  Navier's  hypothesis,  viz. — that  plane  sections  remain  plane 
during  bending.  The  result  obtained  in  the  case  of  beam  7>  is  graphically  repre- 
sented in  Fig.  11,  p.  39. 

Beams  H  to  M  inclusive  give  a  comparison  between  flat  and  round  stirrups  of 
equal  sectional  area. 

Beams  Mt  Nt  0  allow  of  the  study  of  the  effect  of  the  splitting  up  to  the  trans- 
verse reinforcement  into  a  greater  or  less  number  of  stirrups. 


REINFORCED   CONCRETE 


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The  cracks  observed  during  the 
hardening  under  load  were  only 
visible  to  the  magnifying  glass 
after  unloading.  During  the 
loading  tests  a  maximum  load  of 
7'6  tons  or  a  moment  of 
11-22  foot-tons  produced  new 
fissures  and  extended  the  old 
ones  into  the  beam. 

Under  a  total  load  of  7-6  tons  or 
a  bending  moment  of  11-22  foot- 
tons  a  fissure  on  the  tension  side 
of  the  beam  appeared,  and 
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one  end. 

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tons  two  cracks  on  the  tension 
side  appeared,  and  under  a  load 
of  10-08  tons  or  a  bending 
moment  of  14-88  foot-tons  the 
beam  failed  by  cracking  all  over. 

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TESTS   OF   BEAMS 


39 


The  influence  of  the  percentage  of  vertical  reinforcement  may  be  studied  in 
beams  M,  P  and  Q. 

The  comparison  of  vertical  stirrups  with  reinforcements  inclined  at  45  degrees 
may  be  made  in  beams  Q,  R,  S  and  T. 


The  utility  of  returning  the  reinforcements  at  the  extremities  was  studied  in 
beams  /,  U,  V  and  W. 

Beams  V  and  W  were  also  intended  to  show  the  condition  of  the  concrete  in  a 
reinforced  concrete  beam  after  it  had  been  stressed. 

Table  No.  13  gives  an  indication  of  the  quality  of  the  cement  used  in  the  various 
beams.  In  every  case  a  good  result  was  obtained  in  the  soundness  tests. 


40 


REINFORCED   CONCRETE 
TABLE  No    13. 


Time  of  Setting  in  Humid  Air. 

Average  Tensile  Strength  of 
Neat  Cement  (Ibs.  per 
square  inch). 

Commencement. 

Termination. 

7  days. 

28  days. 

84  days. 

Beams  A  —  G    . 

20  minutes 

4J-  hours 

370 

518 

687 

Beams  H—  U 

3  hours 

5J  hours 

549 

653 

646 

Beams  V  and  W 

If  hours 

6J  hours 

469 

550 

654 

Diagram  for  Final  Loading. 


Diagram  For  Initial  Loading. 


Deformations.  Elongations  or  Shortenings.     Indicated  Thus. 
Observed  Deflections  at  Middle  of  Span .  „ 

Scale  to  Deformations. 

TO     0-01  002  003  004  005  006  007  008  009  010 
1       I        I        1       1       I        1        I       I        1       1 


020  per  Cent  of 

" 


DOS 


4- 


Scale  to  Deflections, 


4- 


03/rfcftes 


FIG.  12. 


The  steel  used  was  mild  steel,  having  a  practical  limit  of  elasticity  varying  with 
the  diameter  of  the  rod  of  from  15  to  20  tons  per  square  inch,  a  breaking  strength 


TESTS   OF   BEAMS 


41 


of  from  23  to  28  tons  per  square  inch,  and  an  elongation  of  from  17  per  cent,  to  34 
per  cent,  on  a  length  of  7*87  inches. 

In  addition  to  the  information  given  in  Table  No.  1 2,  the  actual  strains  on  the 
tension  and  compression  faces  and  at  the  neutral  line  were  measured  and  also  the 
variations  in  length  due  to  the  setting  of  the  concrete  in  many  of  the  beams. 
These  are  fully  recorded  in  Chapter  IV.  of  the  French  edition  of  the  Report. 

In  the  case  of  beam  M,  the  extension  and  shortening  of  the  concrete  on  the 
tension  and  compression  faces  respectively  at  the  level  of  the  reinforcements 


Initial    Loading        *       § 

<:>       '"?  \s 

Tensile  Strain  (7.)  of  Concrete  on  Line  Inclined  45  °    Indicated  Thus      


Elongation  of  the  Tension  Reinforcement. 
Deflection  of  Beam. 


Scale  to  Elongation  of  Reinforcement  a.nd  Tensile  Strair 
0     apt  002  003  004  005  006  007  008  O09  010 


longa.tic 
006  007 
~\ 1       I        I        I       I 


•rCent  of 


Inches  0/0 


Scale  lo  Deflection 
0  010 


030  Inches 


FIG.  13. 

measured  on  a  length  of  3-28  feet,  where  the  bending  moment  was  uniform,  together 
with  the  observed  deflections  at  the  middle  of  the  span,  are  given  in  Fig.  1 2. 

In  the  case  of  beam  Q,  the  deflection  at  mid  span,  the  elongation  of  the  tension 
reinforcements  measured  on  a  length  of  19'68  inches,  and  the  elongation  on  a  line 
inclined  at  45°  to  the  length  of  the  beam  are  graphically  represented  in  Fig.  13. 

The  elongations  on  a  line  inclined  at  45°  were  measured  on  a  length  of  19*68 
inches  and  are  stated  as  percentage  alterations  of  original  length,  and  are  plotted  in 
the  curve  in  Fig.  13  marked  "  Tensile  Strain  (°/0)  of  Concrete  on  Line  inclined  45C 


;o  »  1 


1  In  the  French  edition  this  curve  was  marked  simply  "  Shear  Strain."  Monsieur  Mesnager 
has  pointed  out  to  me  that  this  is  an  error  and  that  the  actual  shear  strains  are  double  the  values 
given  by  the  curve.  That  is  clearly  so,  since  in  an  elastic  material  subject  to  a  pure  shear  the 
shear  strains  are  each  very  approximately  double  the  tensile  strains  measured  on  a  line  at  45°  to 
the  directions  of  the  shears.  Consequently  the  shear  strain,  measured  in  radians,  has 
represented  by  the  figures  given  divided  by  50. — N.M. 


42 


REINFORCED   CONCRETE 
10.  Bending  of  Flat  Slabs. 


Thirteen  slabs,  each  3-94  inches  deep  and  19'68  inches  wide,  reinforced  with 
four  rods  at  4 "72-inch  centres  and  placed  in  the  slab  with  0'79  inches  clear  between 
the  rods  and  the  lower  face  of  the  slab,  were  tested  to  destruction  in  order  to 
compare  the  resistances  obtained  under  the  various  conditions  described  in  Table 
No.  1 4,  in  which  a  resume  of  the  results  is  also  given. 


FIG.  14. 

The  sand  used  weighed  99  Ibs.  per  cubic  foot,  of  which 
27*4  per  cent,  was  from  0*197  inches  diameter  to  O079  inches  diameter, 
59-6  „  „         0-079         „  „  0-0197     „ 

13-0          „  „         0-0197       „  „  0-0 

and  contained  6 '2  per  cent,  by  weight  of  moisture. 

The  gravel  used  weighed  89'1  Ibs.  per  cubic  foot,  and 

10 '4  per  cent,  was  from  0'984  inches  to  0*787  inches  diameter. 
75-6  „          „  0-787          „        0-394       „ 

14-0  0-394  0-197 


V<-  -4-72'-  ->*--4-72"->*-  *  72"-  tu2 -76* 

i  jji  i  i  j  j  ,  .  -j--.     ' j-     J J 


44  265         706 


IS88        2029 


3352        3733        4234 


SSS7        5998 


Total    Loa.ds   applied    to  Slab  in   Pounds 

FIG.  is. 


The  gravel  contained  6'8  per  cent,  of  its  weight  of  sand  and  3*8  per  cent,  of 
its  weight  of  water. 

The  cement  used  was  of  medium  setting  time,  setting  in  4J  hours,  and  giving 
a  resistence  to  tension  of  480  Ibs.  per  square  inch  after  seven  days  and  580  Ibs. 
per  square  inch  after  twenty-eight  days.  Slab  No.  14  was  made  of  a  variety  of  lime 
setting  in  eighteen  hours  and  giving  a  resistance  to  tension  of  1 40  Ibs.  per  square 
inch  after  seven  days,  207  Ibs.  per  square  inch  after  fourteen  days,  and  304  Ibs. 
per  square  inch  after  eighty-four  days, 


TESTS   OF   FLAT   SLABS 


43 


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46  REINFORCED   CONCRETE 

The  reinforcements  of  0*197  inches  diameter  were  of  iron  having  a  limit  of 
elasticity  of  17  tons  per  square  inch,  a  breaking  strength  of  25  tons  per  square 
inch,  and  an  elongation  of  14  per  cent,  on  7 '8 7  inches. 

The  reinforcements  of  0*394  inches  and  0*591  inches  diameter  were  of  mild 
steel  having  a  limit  of  elasticity  of  17  tons  per  square  inch,  a  breaking  strength 
of  25 J  tons  per  square  inch  and  an  elongation  of  26  per  cent.,  with  a  modulus  of 
elasticity  of  14,200  tons  per  square  inch. 

The  slabs  were  left  in  the  open  air  from  the  date  of  manufacture  till  the  date 
of  the  test ;  and  the  loads  were  applied  as  indicated  in  Fig.  14. 

The  load  in  the  case  of  slab  No.  1 1  was  applied  in  twenty  minutes ;  in  the 
other  cases  the  time  varied  from  fifty-five  minutes  to  2£  hours. 

From  zero  load  up  to  the  first  load  given  in  the  table,  the  deflection  in  each 
case  follows  a  straight-line  law,  and  is  directly  proportional  to  the  load  applied. 
For  loads  beyond  the  first  load  given,  the  deflection  continues  generally  to  obey  a 
straight-line  law,  but  the  rate  of  increase  of  the  deflection  is  much  greater  than  up 
to  that  load.  The  results  from  all  the  slabs  are  very  similar,  and  Fig.  15  gives 
the  deflection  diagram  for  slab  No.  5,  which  is  typical  of  the  others. 


11.  Experiments  on  Ribbed  Slabs. 

Two  floors  were  constructed  each  of  span  about  9  feet  6  inches,  one  4  feet 
wide,  the  other  6  feet  6  inches,  and  each  stiffened  by  one  central  rib.  The 
floors  were  2*36  inches  deep  and  the  ribs  had  7*50  inches  of  additional  depth,  and 
were  6  inches  wide. 

In  the  case  of  the  floor  6  feet  6  inches  wide  the  rib  had  tension  reinforcement 
only  consisting  of  four  rods,  placed  two  vertically  above  two,  each  of  0*87  inch 
diameter  with  0*5  inch  clear  between  the  rods  and  0*8  inch  clear  between  the 
rod  and  the  lower  face  of  beam,  and  having  sheet-iron  stirrups  of  1*575  inches 
X  0*085  inch  at  about  4j  inches  centres  extending  nearly  to  the  upper  surface  of 
the  floor.  The  floor  was  reinforced  in  the  middle  of  its  depth  by  rods  of  0*394  inch 
diameter  spaced  at  about  4J  inches  centres ;  the  ribs,  very  slightly  increased  in 
depth,  were  returned  along  the  ends  of  the  slabs  to  form  a  continuous  support  for 
the  floor.  The  test  load  was  applied  along  a  width  of  9  inches  centrally  over  the 
rib,  and  was  uniformly  distributed  in  the  direction  of  the  length  except  for  two 
short  gaps  at  the  centre,  where  strain-recording  instruments  were  placed.  A 
maximum  load  of  20*2  tons  was  placed  on  the  slab  a  little  less  than  six  months 
after  manufacture.  At  this  load  a  noticeable  crack  extended  across  the  tension 
side  of  slab  and  rib.  Measurements  of  the  deflection  were  not  made,  but  the 
actual  strains  in  the  structure  wrere  carefully  measured.  These  are  fully  recorded 
in  the  French  edition,  p.  240. 

In  the  case  of  the  floor  4  feet  wide,  the  rib  had  tension  reinforcement  consisting 
of  four  rods,  each  0*787  inch  diameter,  placed  two  vertically  above  two,  spaced 
and  with  sheet  stirrups  as  in  the  other  floor.  The  method  of  reinforcing  and  sup- 
porting the  floor  during  the  test  was  exactly  as  in  the  floor  previously  described, 
but  the  load  in  this  "case  was  uniformly  spread  over  the  whole  floor.  A  total  load 
of  15*26  tons  was  applied,  corresponding  to  a  load  of  7*87  cwts.  per  square  foot  of 
total  surface,  and  remained  in  position  for  twenty-three  hours.  After  eighteen 
hours'  application  of  the  load  no  further  straining  was  observed  and  no  cracks 
of  any  kind  were  observed,  and  on  removing  the  load  the  strains  almost  entirely 


TESTS   OF   RIBBED   SLABS  47 

The  measured  strains  are  given  in  the   French  edition,  p.  238,  and  a  diagram 
graphically  representing  these  strains  is  reproduced  in  Fig.  1 6. 


The  materials  employed  were  similar  in  character  to  those  used  in  the  manu- 
facture of  the  experimental  beams. 


48 


REINFORCED   CONCRETE 


15-75" •> 


12.  Tests  of  Columns  and  Prisms  in  Compression. 

1.   9  Columns,  each  1 6* 4  feet  long. 

1.  Nine  columns,  each  16 -4  feet  long,  seven  15 '7 5  inches  square  and  two  9 -8 4 
inches  square,  were  tested  to  destruction.  Fig.  16A  indicates  the  typical  cross 
section  of  the  columns,  particulars  of  which  are  given  in  Table  No.  16  (pp.  50 — 51) 
and  Table  No.  17  (p.  49)  together  with  a  resume  of  the  results  obtained. 

Each  column  was  reinforced  with  four  round  bars  placed  one  at  each  corner,  so 
as  to  leave  about  0*9  inch  clear  between  each  face  of  the  column 
and  the  surface  of  the  reinforcement.  The  reinforcing  rods  were 
united  by  sheet  interties  0-118  inch  thick,  placed  19*68  inches 
apart  in  the  column  and  9 '8 4  inches  from  either  end. 

The  columns  were  manufactured  under  conditions  pertaining 
in  practice.     Moulding  was  effected  on  the  flat. 

The  concrete  used  consisted  of  6  cwts.  of  Portland  cement 
to  14 '3 5  cubic  feet  of  siliceous  Seine  sand  passing  through  holes 
0-197  inch  in  diameter,  and  28*7  cubic  feet  of  siliceous  Seine 
gravel  passing  through  holes  0'984  inch  in  diameter  and  retained  on  holes  0'197  inch 
in  diameter.  These  materials  were  mixed  with  water,  8 -2  per  cent,  of  the  weight  of 
the  mixture  of  dry  materials.  The  quantities  used  were  obtained  by  weighing,  taking 
account  of  the  humidity  of  the  sand,  about  5  per  cent,  by  weight,  and  of  the  gravel, 
about  3 '5  per  cent,  by  weight  as  well  as  the  quantity  of  sand  contained  in  the 
gravel,  9  per  cent,  by  weight  of  the  latter.  The  granulometric  composition  of  the 
sand  and  gravel  was  very  similar  to  that  of  the  materials  described  on  p.  30. 

The  cement  used  commenced  setting  in  air  in  four  hours  and  setting  was  com- 
pleted in  6J  hours,   and  it  stood  the  soundness  tests  satisfactorily.     The  average 
resistance  to  tension  of  briquettes  of  neat  cement  was  528  Ibs.  per  square  inch  after 
seven  days  and  576  Ibs.  per  square  inch  after  twenty-eight  days. 
The  quality  of  the  reinforcement  is  indicated  in  Table  No.  15. 

TABLE  No.   15. 


FIG.  16A. 


— 

— 

Apparent 
Limit  of 
Elasticity. 

Breaking 
Load  per 
square  inch 
of  Initial 
Section. 

Elongation 
per  cent, 
after 
Rupture  ;  on 
7-87  inches. 

Modulus  of 
Elasticity. 

Rod  of  1-77  inches 
diameter. 

Mild  steel 

Tons  per 
square  inch. 
14-5 

Tons. 
22-8 

32% 

Tons  pei- 
square  inch. 
13,650 

Rods  0-47  inch  to 
1'26  inches  dia- 
meter. 

Do. 

17-9 

25-5 

28% 

14,500 

Sheets  0-118  inch 
thick. 

Do. 

16-9 

22-6 

26-5% 

— 

Do.  ... 

Iron 

16-5 

21-6 

15% 

— 

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52 


REINFORCED   CONCRETE 

2.   12  prisms  7 -87"  X  7'87"  X  3'28  feet  long. 


These  prisms  were  constructed  of  6  cwts.  Portland  cement,  14*35  cubic  feet  Seine 
sand  passing  through  0'197  inch  diameter  holes,  and  28-7  cubic  feet  Seine  gravel 
passing  through  0'984  inch  diameter  holes.  In  six  of  the  prisms  the  concrete  was 


0  121282    564     846    1128    1410    1692   1514 
Load  Pounds  per  Sq.  Inch. 


age 
00 


19. 


0       282    564    846     1128    1410     1692    1974    2256  2538  2821    3104 


Shortening  as  Percentage  of  Original  Length. 
0-01  002  0-03  004  005  006  007  008  009  0-10  01 

/ 

// 

z 

/ 

Fig. 

20. 

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282     564     846    1128    1410    1692    1974    2256  2538   2821    31 
Load  Pounds  per  Sq.  Inch. 

mixed  with  water  amounting  to  1 1  '2  per  cent,  of  the  weight  of  the  dry  materials,  and 
was  consequently  of  soft  consistency  and  was  simply  poured  into  the  moulds.  In 
the  other  six  prisms  8 '2  per  cent,  of  water  was  used  and  the  concrete  rammed. 

Four  prisms  were  made  without  reinforcement ;  in   two  of  these  the  concrete 
was  simply  poured,  and  in  the  other  two  rammed. 


TESTS   OF   PRISMS 


53 


Four  prisms  were  reinforced  longitudinally,  each  by  four  rods  0*709  inch 
diameter,  placed  at  0*787  inch  from  each  face  and  united  by  three  sheet  interties 
1-575  inches  X  0-118  inch  thick,  the  extreme  ties  being  placed  about  6|  inches 
from  the  ends.  The  longitudinal  reinforcement  amounted  to  2 '5 4  per  cent,  of  the 
total  area,  and  the  interties,  reduced  to  an  equivalent  rod  of  the  same  volume, 
0*65  per  cent.,  or  together  to  a  total  of  3*19  per  cent. 

Four  prisms  were  spiralled  with  a  wire  0*236  inch  diameter  at  0-79  inch 
pitch,  of  a  mean  diameter  of  7*24  inches.  In  addition  there  were  six  longitudinal 
rods,  each  0'354  inch  diameter,  placed  inside  the  spiralling.  An  equivalent  rod 
of  the  same  volume  as  the  spiralling  would  have  an  area  2*04  per  cent,  of  the  total 
area  of  the  prism,  and  adding  0*95  per  cent,  as  the  percentage  of  the  longitudinal 
reinforcement,  the  total  reinforcement  is  2*99  per  cent.,  roughly  the  same  as  for 
the  longitudinal  bars.  The  spiralling  was  applied  in  sections  comprising  seven  to 


7-16"    -- 


FIG.  21. 


nine  helices,  the  sections  being  simply  superposed  after  having  reduced  the  last  spiral 
at  each  end  to  half  pitch. 

The  reinforcement  was  of  mild  steel  of  ordinary  quality.  The  rods  of 
0*354  inch  diameter  had  an  apparent  limit  of  elasticity  of  18  tons  per  inch2, 
an  ultimate  strength  of  26  tons  per  square  inch,  and  a  total  elongation  of  26  per 
cent,  on  7*87  inches. 

In  each  case  the  prisms  were  removed  from  the  moulds  forty-eight  hours  after 
manufacture,  and  kept  moist  by  watering  for  three  days.  One  of  each  type  was 
then  kept  dry  in  the  air,  the  other  of  that  type  was  kept  under  a  bed  of  sand 
frequently  watered.  A  resume  of  the  results  is  given  in  Table  No.  18,  pp.  54 — 56. 

In  Fig.  17  the  results  of  the  tests  of  the  prisms  with  the  three  types  of  rein- 
forcement are  exhibited  graphically.  The  three  prisms  in  this  group  were  made 
from  the  same  wet  mixture,  and  similarly  treated  after  moulding,  viz.,  kept  in  a 
dry  atmosphere  till  the  date  of  the  tests. 

In  Fig.  18  the  results  obtained  are  exhibited,  when  the  prisms  from  a  similar 
wet  mixture  are  kept  moist  after  moulding. 

Figs.  19  and  20  represent  graphically  the  corresponding  results  when  a  dry 
mixture  is  used  and  carefully  rammed,  and  the  prisms  kept  in  the  dry  and  kept 
moist  respectively. 


54 


REINFORCED   CONCRETE 


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TESTS   OF   PRISMS 


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TESTS   OF   COLUMNS 


57 


3.   24  columns  from  6*5 6  feet  long  to  13*12  feet  long. 

The  columns  manufactured  had  a  section  either  square  of  7*16  inches  side  or 
octagonal  with  the  diameter  of  the  inscribed  circle  7*87  inches,  as  shown  in 
Fig.  21  (p.  53). 

The  series  of  square  columns  comprised  columns  not  reinforced,  and  columns 
reinforced  longitudinally  as  shown  on  the  cross  section.  The  interties  were  placed 
at  13  inches  centres  and  6|  inches  from  the  ends. 

The  series  of  octagonal  columns  included  only  columns  spiralled  with  a  metallic 
spiral  rolled  at  varying  pitches  to  an  exterior  diameter  of  7 '48  inches. 

In  each  case  the  longitudinal  reinforcements  were  about  a  quarter  of  an  inch 
shorter  than  the  columns,  and  they  were  not  flush  at  either  extremity. 

All  the  columns  were  cast  vertically  and  were  manufactured  by  workmen  under 
the  conditions  met  with  in  actual  works. 

The  columns  were  made  in  two  series  :  (a)  containing  7  cwts.  Portland  cement, 
14'3  cubic  feet  Seine  sand  passing  through  a  sieve  with  holes  0'197  inch 
diameter,  and  28'7  cubic  feet  of  Seine  gravel  passing  through  a  hole  of  0'984  inch 
diameter  ;  and  (b)  containing  10  cwts.  Portland  cement  to  those  quantities  of  sand 
and  gravel. 

The  water  employed  in  gauging  was  8*3  per  cent,  of  the  weight  of  the  dry 
mixture  in  the  former  case,  and  9  per  cent,  in  the  latter.  The  resulting  concrete 
was  plastic ;  that  is  to  say,  that  after  being  well  worked  up  it  moistened  on  striking 
with  the  flat  of  a  spade.  During  the  first  fortnight  of  hardening  the  columns 
were  watered  slightly  every  two  or  three  days. 

The  columns  were  weighed  in  order  to  determine  the  approximate  density  of 
the  concrete,  and  the  weights  per  cubic  foot  are  given  in  Table  No.  19,  and  for 
purposes  of  comparison  the  weights  per  cubic  foot  of  the  prisms  of  Series  2  (p.  52) 
are  added. 

TABLE  No.   19. 


6  cwts.  Portland  Cement. 

7  cwts. 

10  cwts. 

Portland  Cement. 



Kept  in  Air. 

Kept  Moist. 

Rammed  and 

Rammed  and 

Poured. 

Rammed. 

Poured. 

Rammed. 

Kept  in  Air. 

Kept  in  Air. 

Non-reinforced 

143-5 

150-2 

146-9 

152-5 

149-0 

148-0 

Reinforced  to  total  per- 

— 

.  — 

— 

155-1 

154-7 

centage  of  2  '13. 

Reinforced  to  total  per- 

153-0 

158-f) 

156-9 

162-2 

— 

— 

centage  of  3-19. 

Reinforced  to  total  per- 

— 

—       .       — 

— 

166-3 

164-1 

centage  of  4*94. 

The  extremities  of  each  column  were  ground  and  rendered  as  exactly  plane  and 
parallel  as  possible,  and  the  load  was  applied  directly  by  the  heads  of  the  hydraulic 
press  with  the  interposition  of  a  sheet  of  cardboard  0'079  inch  thick. 

The  reinforcements  were  of  mild  steel  or  of  iron,  of  somewhat  varying  quality. 
Rods  of  mild  steel  of  0'304  inch  diameter  had  an  elastic  limit  of  14'6  tons  per 
square  inch,  a  breaking  strength  of  2 3 -2  tons  per  square  inch,  and  a  percentage 


58 


REINFORCED   CONCRETE 


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Unita.1  Compressive  Stress  in  ibs.  per  Sy.  Inch. 


TESTS   OF   COLUMNS  59 

elongation  on  7*87  inches  of  25  per  cent.,  whilst  rods  of  0*315  inch  diameter  had 
an  elastic  limit  of  22*5  tons  per  square  inch,  and  an  ultimate  strength  of  29  tons 
per  square  inch,  with  an  elongation  of  21*5  per  cent,  in  7*87  inches,  all  the  varieties 
of  iron  and  steel  used  being  between  these  values. 

The  cement  used  stood  the  soundness  tests  satisfactorily ;  setting  commenced 
in  2  hours  40  minutes,  and  was  complete  in  5  hours  40  minutes.  Briquettes  of 
neat  cement  had  a  mean  resistance  to  tension  of  535  Ibs.  per  inch2  after  seven  days, 
and  578  Ibs.  per  inch2  after  twenty-eight  days. 

Fig.  22  shows  graphically  the  results  obtained  with  columns  6 '5  6  feet  long 
and  13 '12  feet  long,  manufactured  in  both  cases  with  a  concrete  composed  of 
7  cwts.  of  Portland  cement,  28'7  cubic  feet  of  gravel,  and  14'3  cubic  feet  of 
sand. 

Fig.  23  shows  the  results  obtained  with  columns  of  a  similar  length,  and  with  a 
mixture  of  10  cwts.  of  Portland  cement  to  28*7  cubic  feet  of  gravel,  and  14*3  cubic 
feet  of  sand. 

Fig.  24  shows  the  results  obtained  with  spiralled  columns  of  various  lengths 
manufactured  with  concretes  containing  7  cwts.  and  10  cwts.  respectively  of 
Portland  cement,  to  28'7  cubic  feet  of  gravel  and  14*3  cubic  feet  of  sand. 

The  graphs  in  the  above  figures  do  not  show  the  point  at  which  the  column 
actually  collapsed,  but  simply  the  point  at  which  the  readings  were  discontinued 
owing  to  the  virtual  failure  of  the  column. 

The  rupture  of  the  columns  having  for  the  most  part,  and  particularly  for  those 
of  concrete  with  10  cwts.  of  cement,  occurred  near  the  extremity  corresponding 
to  the  upper  end  of  the  column  during  moulding,  experiments  were  carried  out  to 
discover  to  what  extent  the  resistance  of  the  concrete  might  vary  in  columns 
moulded  vertically  without  special  precautions. 

In  the  case  of  the  columns  6*56  feet  long,  a  prism  18*9  inches  long  was  cut 
from  the  base  and  tested  by  crushing.  In  the  case  of  the  concrete  containing 
7  cwts.  of  cement,  the  prisms  from  the  base  showed  an  increase  in  crushing  strength 
of  420  Ibs.  per  square  inch  over  the  figure  for  the  whole  column.  In  the  case 
of  the  concrete  containing  10  cwts.  cement  the  figure  was  1,850  Ibs.  per  square 
inch. 

In  the  case  of  the  columns  13'12  feet  long,  prisms  were  cut  from  the  base  and 
from  a  part  of  the  column  3  feet  from  its  upper  end  during  moulding.  The 
prisms  from  the  base  had  570  Ibs.  per  inch2  greater  resistance  to  crushing  than  the 
upper  prism,  and  about  1,360  Ibs.  per  inch2  greater  resistance  to  crushing  than  the 
whole  column  for  a  concrete  containing  7  cwts.  Portland  cement,  whilst  for  a  con- 
crete containing  10  cwts.  Portland  cement  these  figures  were  1,350  Ibs.  per  inch2 
and  2,570  Ibs.  per  inch2  respectively. 

13.  Compression    Tests    of   Spiralled    Mortar    and   Concrete. 

1.  Prisms  in  Cement  Concrete,  arranged  by  M.   Considere. 

These  prisms,  of  octagonal  section  of  29'45  square  inches  area  and  1*64  feet 
long,  were  submitted  to  compression  tests  carried  to  rupture,  the  deformations 
being  measured. 

The  results  are  given  in  Table  No.  20  (p.  62). 


REINFORCED   CONCRETE 


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TESTS   OF   COLUMNS 


61 


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Unital  Compressive  Stress  in  Lbs.  per  Sq.  Inch. 


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REINFORCED   CONCRETE 


TABLE  No.   20. 


Description. 

Load  Applied 
to  Spiralled 
Core, 
Ibs.  perinch2 

Shortening 
per  cent,,  of 
Original 
Length. 

Remarks. 

1.  Prism  not  reinforced  ;  age, 
4  months.  Stress  reckoned 
on  total  section. 

307 
1,050 
1,168 

0-0128 
0-0680 

Modulus  of  Elasticity  : 
From  165  Ibs.  per  inch2  to  750 
Ibs.  per  inch'2  =2-18  X    10*5 
Ibs.  per  inch2. 
From  58  Ibs.  per  inch2  to  750 
Ibs.  per  inch2  =  2-11  x  106 
Ibs.  per  inch.2 
Rupture. 

2.  Prism  reinforced  with  a  rod 
0-236  inch  diameter, 
spiralled  to  a  pitch  of 
1-18  inches,  and  to  an 
exterior  diameter  of  5  '51 
inches.  The  sectional  area 
of  the  reinforced  core  was 
26-4  square  inches. 

344 
1,502 
65 
1,502 
3,160 

5,770 

0-0160 
0-0880 
0-0320 
0-9400 
1-2740 

Permanent  deformation. 

Covering  of  spirals  progressively 
detached. 
Prism   completely  deformed  into 
S  shape. 

3.  Prism  reinforced  with  an  iron 
rod  0'161  inch  diameter, 
spiralled  to  a  pitch  of  0*59 
inch,  and  to  an  exterior 
diameter  of  5  -51  inches. 
The  sectional  area  of  the 
reinforced  core  was  2  6  -4 
square  inches  ;  the  pitch 
of  the  spirals  was  a  little 
irregular,  the  pitch  attain- 
ing -67  inch  in  places. 

344 
1,502 
65 
1,502 
3,610 

6,016 

0-016 
0-0740 
0-016 
0-0660 
0-6560 

External    covering   of    spiralling 
detached  bit  by  bit. 
Maximum    load    of     which    the 
testing    machine   was   capable. 
Column  not  broken. 

4.  Prism  reinforced  with  a  rod 
0'236  inch  diameter, 
spiralled  to  an  external 
diameter  of  5  '51  inches, 
and  to  a  pitch  of  1'063 
inches.  Average  section 
of  core  =  26  -4  square 
inches. 

344 
1,502 
65 
1,502 
3,610 

5,635 

0-0020 
0-0720 
0-0080 
0-0768 
1-5640 

Permanent  deformation. 

External    covering  of    spiralling 
detached  bit  by  bit. 
Rupture. 

5.  Prism  reinforced  longitudi- 
nally with  8  rods,  0'315 
inch  diameter,  giving 
sensibly  the  same  per- 
centage of  metal  as  in 
the  preceding  spirally 
armoured  prism.  The 
stresses  given  are  reckoned 
on  the  total  section  of 
29  '45  square  inches. 

1,530 
1,835 

Cracking  commenced. 
Complete  failure. 

6.  Non-reinforced  prism  of 
29  '45  square  inches  area. 
Stress  reckoned  on  total 
area. 

825 

Complete  failure. 

NOTE. — In  Prisms  2,  3  and  4  the  transverse  swelling  of  the  spirals  was  measured,  but 
no  conclusive  results  were  obtained. 


TESTS  OF  SPIRALLED  PRISMS  63 


2.   Six  Prisms  in  Cement  Concrete,  as  desired  by  M.   Consider e. 

Six  octagonal  prisms  of  about  15*5  square  inches  cross  sectional  area  and 
1*64  feet  long  were  made. 

Three  of  the  prisms  were  of  a  mixture  of  8  cwts.  of  Portland  cement  to 
9*56  cubic  feet  of  sand,  screened  to  0*197  inch  diameter,  and  28*7  cubic  feet 
of  gravel  (0*197  inch  to  0*984  inch  diameter),  and  water  amounting  to  9 '3  per 
cent,  of  the  weight  of  the  dry  materials,  was  used  as  being  necessary  and  sufficient 
to  obtain  a  plastic  consistency. 

The  other  three  were  composed  of  a  mixture  of  10*7  cwts.  of  Portland  cement 
to  the  above  quantities  of  sand  and  gravel  and  9 -8  per  cent,  of  water. 

In  the  former  series  of  three  prisms,  two  were  spiralled  at  a  pitch  of  0*55  inch 
for  about  one-quarter  of  the  length  from  either  end  and  0*79  inch  for  the 
remaining  portion  in  the  middle.  In  the  latter  the  pitch  of  the  spirals  for 
one-fifth  of  the  length  of  the  column  at  either  end  was  0*39  inch,  whilst 
the  middle  portion  was  spiralled  to  0*59  inch  pitch.  The  spiralling  was  of 
iron  wire  0*169  inch  diameter,  and  the  external  diameter  of  the  spirals  was 
3*94  inches.  In  addition,  the  prisms  were  reinforced  each  with  eight  rods 
of  0*169  inch  diameter,  placed  in  the  interior  of  the  spirals  and  in  contact 
with  them. 

The  two  spiralled  prisms,  containing  8  cwts.  Portland  cement,  were  loaded 
by  small  increments  to  a  stress  of  1,300  Ibs.  per  square  inch  of  total  section,  and 
showing  under  that  stress  an  average  shortening  of  0*0652  per  cent,  of  their 
original  length,  with  an  average  permanent  deformation  of  0*0244  per  cent,  of 
their  original  length  when  the  load  was  removed.  This  permanent  deformation 
increased  slightly  when  the  load  was  reapplied  and  removed. 

From  one  of  the  prisms  the  crust  of  concrete  covering  the  spiral  reinforcement 
was  removed  down  to  the  centre  of  the  spiralling  rods,  and  a  compression  was 
again  applied  and  removed  and  the  process  repeated.  At  each  repetition  the 
stress  was  carried  higher  and  the  permanent  deformation  measured.  At  a  stress 
of  2,366  Ibs.  per  square  inch  of  the  core  the  shortening  was  0*16  per  cent,  of  the 
original  length,  whilst  the  permanent  deformation  was  0*074  per  cent.  At  a  stress 
of  9,270  Ibs.  per  square  inch  the  deformation  was  2*4  per  cent.,  and  the  permanent 
set  amounted  to  1*81  per  cent.  The  maximum  stress  applied  was  9,480  Ibs.  per 
square  inch,  but  as  the  prism  threatened  to  break,  this  load  was  removed  before 
readings  were  taken.  The  spiralling  was  then  stripped  and  the  core  tested. 
Crushing  took  place  at  870  Ibs.  per  square  inch.  The  age  of  the  concrete  at  test 
was  about  ten  weeks. 

In  the  other  prism  no  further  compression  tests  were  made  as  above,  but  the 
spiralling  was  also  removed  and  compression  applied.  Crushing  took  place  at  a 
stress  of  1,670  Ibs.  per  square  inch. 

The  third  prism  of  this  mixture  was  made  without  reinforcement  for  purposes  of 
comparison,  and  failed  at  1,142  Ibs.  per  square  inch. 

Two  of  the  prisms  of  the  mixture  containing  10*7  cwts.  Portland  cement,  one 
reinforced  and  the  other  not  reinforced,  were  tested.  The  concrete  was  about  four 
months  old  at  test  and  had  been  immersed  in  fresh  water  for  six  weeks  previous 
to  it. 

The  reinforced  prism  at  a  stress  of  6,370  Ibs.  per  square  inch  of  the  spiralled 
core  underwent  a  shortening  of  0*582  per  cent,  of  its  original  length,  and  on  the 
load  being  removed  showed  a  permanent  deformation  of  0*342  per  cent.  The 


64  REINFORCED   CONCRETE 

prism  ultimately  perished  by  buckling   under   a   stress  of   12,700  Ibs.  per  square 
inch  of  the  section  of  the  core. 

The  prism  not  reinforced  failed  at  a  stress  of  2,235  Ibs.  per  square  inch  of 
total  section. 

3.   Eight  Cylinders  of  Mortar  Spiralled  for  Compression  Tests. 

These  cylinders  had  a  mean  diameter  of  3 '3  inches  and  a  length  of 
23-23  inches,  but  in  consequence  of  the  low  modulus  of  elasticity  of  the 
mortar  they  showed  a  tendency  to  fail  readily  by  buckling.  Some  were  cut 
and  tested  in  shorter  lengths,  but  it  has  not  been  thought  fit  to  give  the 
detailed  results  owing  to  the  impossibility  of  making  comparisons. 

The  cylinders  tested  were  spiralled,  either  with  single  spiral,  with  two  con- 
centric spirals  or  with  three  concentric  spirals.  When  of  the  same  length  and 
when  the  columns  failed  by  buckling  the  two  concentric  spirals  only  gave  an 
increased  ultimate  strength  of  about  11  per  cent,  over  the  figure  shown  by  the 
single  spiral.  When,  however,  the  column  failed  more  evenly  by  crushing,  the 
two  concentric  spirals  gave  an  increase  of  24  per  cent,  of  the  crushing  strength 
shown  by  the  single  spiral,  and  the  three  concentric  spirals  showed  an  increase  of 
49  per  cent,  over  the  crushing  strength  shown  by  the  single  spiral.  The  stress  at 
which  the  external  covering  of  concrete  on  the  spirals  began  to  flake  off  was  not 
appreciably  affected  by  the  addition  of  the  concentric  spiralling.  This  stress  for 
cylinders  six  months  old  was  about  4,550  Ibs.  per  square  inch  of  the  total  section. 

4.   Cylinders  of  Annular  Section  in  Cement  Mortar. 

Three  cylinders,  each  2 3 '6 2  inches  long,  composed  of  mortar  containing  6  cwts. 
of  Portland  cement,  11 '8  cubic  feet  of  Seine  sand  screened  to  0'197  inch  diameter 
and  gauged  with  water  amounting  to  15 '7  per  cent,  of  the  weight  of  the  dry 
materials.  The  cylinders  were  kept  in  air  for  ten  weeks  after  manufacture ; 
they  were  then  immersed  in  fresh  water  for  six  weeks,  from  which  they  were 
taken  for  testing  purposes. 

The  particulars  of  the  cylinders  and  the  results  of  the  tests  are  given  in 
Table  No.  21. 

5.   Two  Spiralled  Prisms  from  the  Experimental  Bridge,  builtt  by  M.  Considere. 

These  prisms  were  taken  from  the  upper  boom  of  the  above  bridge,  which  was 
of  the  bowstring  type.  They  were  of  octagonal  section,  inscribed  circle  9 '8 4  inches 
diameter,  giving  a  total  cross  section  of  80' 2 9  square  inches  and  an  area  of  spiralled 
core  of  48'67  square  inches. 

The  first  prism  tested  was  41  inches  long.  Under  a  stress  of  2,842  Ibs.  per 
square  inch  of  the  total  section  the  shortening  was  0'0856  per  cent,  of  the  original 
length,  and  under  a  stress  of  5,684  Ibs.  per  square  inch  of  the  total  area  or  of 
9,380  Ibs.  per  square  inch  of  the  spiralled  core  was  0'2  per  cent.,  whilst  the  outer 
covering  of  concrete  on  the  spirals  began  to  fall  off.  The  maximum  stress  applied 
was  12,690  Ibs.  per  square  inch  of  the  spiralled  core,  at  which  stress  the  bending 
of  the  prism  rapidly  increased.  At  the  time  of  the  test  the  prism  was  about  two 
years  old. 

The  other  prism  was  52  inches  long  and  was  tested  by  the  application  of  a 
load  at  one-third  of  the  diameter  from  one  face.  Up  to  a  stress  of  4,670  Ibs.  per 
square  inch,  reckoned  as  uniformly  distributed  over  the  whole  section,  no  cracking 


TESTS  OF  SPIRALLED  PRISMS 


65 


was  apparent,  and  the  angle  between  the  end  faces  of  the  column  wasO'0087  radians. 
At  a  stress  corresponding  to  10,600  Ibs.  per  square  inch,  if  uniformly  spread  over 
the  core,  the  angular  deformation  was  0*0113  radians,  and  the  column  failed  by  the 
shearing  of  the  concrete  of  the  core. 

6.  Prism  of  Spiralled  Concrete  for  Compression  Test. 

This   prism  of  square   section  of  10*24  inches  side  and  37  inches  long   was 
composed  of  fluid  concrete  poured  without  any  ramming. 

It  was  reinforced   with    a    spiral  of  mild  steel  rod  of  0*472  inch  diameter 


TABLE  No.   21. 


Results  of  Test. 

No. 

External 
Diameter 

Internal 
Diameter 

Area. 

Spiralling. 

Load 
Applied, 
Ibs.  per 

Mean 

Shorten- 
ing per 

Remarks. 

square 

C6nt  of 

inch  of 

Tr»4-ol 

Original 

J.  Ot'ft  1 

Section. 

Length. 

Inches. 

Inches. 

Inches.2 

1. 

7*09 

4*92 

20*52 

Iron  wire  0*189  inch 

441 

0*016 

— 

diameter  in  helical 

2,170 

0*096 

The  cylinder  broke 

pitch  of  0*787  inch. 
External  diameter 

2,570 

in  consequence  of 
the  failure  of  the 

of    spiralling    6*89 

mortar  inside  the 

inches. 

cylinder  owing  to 

' 

want  of  support. 

2. 

7-09 

4*53 

23*34 

Iron  wire  0*189  inch 

2,300 

Do. 

diameter  in  helical 

pitch  of  0*787  inch. 

External  diameter 

of    spiralling   6*69 

inches. 

3. 

4*76 

17*83 

Not  reinforced. 

2,490 

Maximum          load 

supported. 

wound  to  a  mean  diameter  of  8*39  inches  and  to  a  pitch  of  1*024  inches,  giving  a 
percentage  of  4*3,  and  in  addition  in  the  longitudinal  direction  with  seven  bars  of 
mild  steel  of  0*63  inch  diameter  arranged  round  the  inside  of  the  spiral  and  in 
contact  with  it,  giving  a  percentage  of  about  2'1.  The  age  of  the  concrete  at  the 
time  of  the  test  was  about  three  months.  The  load  was  applied  axially  and  the 
first  fissures  appeared  at  a  stress  of  4,040  Ibs.  per  square  inch  of  the  total  area, 
and  the  maximum  stress  supported  was  10,200  Ibs.  per  square  inch  of  the  spiralled 
core.  At  that  stress  the  shortening  was  2  per  cent. 

The  spiralling  was  subsequently  removed  and  the  resistance  to  direct  crushing 
of  the  non-reinforced  concrete  was  found  to  be  1,124  Ibs.  per  square  inch,  measured 
on  a  cylinder  of  6*89  inches  diameter  and  18  inches  long. 

R.C.  F 


66 


REINFORCED   CONCRETE 


7.    Two  Prisms  Reinforced  with  Intertwining  Spirals. 

These  prisms  were  of  the  section  shown  in  Fig.  25  and  were  19 '68  inches  long. 

The  spirals  were  of  mild  steel  wire  0'272  inch  diameter,  rolled  on  a  cylinder 
of  5J  inches  diameter  to  a  pitch  of  1  inch.  Alternate  spirals  were  wound  in 
opposite  directions.  Longitudinal  reinforcements  of  mild  steel  0'315  inch 
diameter  were  placed  as  shown. 

The  concrete  consisted  of  12  cwts.  Portland  cement  to  14 '3 5  cubic  feet  of  sand 
sieved  to  0'197  inch  diameter  and  28'7  cubic  feet  of  gravel.  In  both  cases  the 
moulding  was  done  on  the  flat.  For  prism  No.  1  concrete  of  a  plastic  consistency 
well  rammed  was  employed ;  for  No.  2  a  wetter  concrete  was  used  to  fill  the  mould 
up  to  the  level  of  the  upper  side  of  the  spirals,  of  sufficient  fluidity  to  fill  the  spirals 
without  ramming  between  them,  the  mould  was  then  filled  with  the  mixture  of 
materials  quite  dry  and  rammed  till  the  moisture  appeared  on  the  surface.  The 
prisms  were  kept  in  air  for  the  eight  months  that  elapsed  between  the  time  of 
moulding  and  the  test. 

In  both  cases  at  a  stress  of  4,550  Ibs.  per  square  inch  of  the  total  section  of  the 
prisms,  or  7,110  Ibs.  per  square  inch  of  the  section  of  the  spiralled  core,  the  concrete 


<- 18-5" - ---> 

FIG.  25. 

outside  the  spiralling  began  to  flake  off.  The  maximum  load  carried  by  prism 
No.  1  was  9,730  Ibs.  per  square  inch  of  the  spiralled  core,  whilst  the  maximum 
stress  supported  by  prism  No.  2  was  10,930  Ibs.  per  square  inch  of  the  spiralled 
core.  In  both  cases  the  total  shortening  was  3'6  per  cent,  of  the  original  length. 

14.  Tension  Tests  on  Reinforced  Members. 

Two  tension  members  were  constructed  of  twenty-four  wires  of  steel  surrounded 
by  a  metallic  spiral  as  indicated  in  Fig.  26,  and  encased  for  a  length  of  6*56  feet. 
One  half  of  the  length  of  each  member  was  of  neat  cement,  the  other  half  of  mortar. 

In  member  No.  1  the  diameter  of  the  longitudinal  wires  was  *177  inch,  giving 
a  percentage  reinforcement  of  5*9.  The  wires  were  placed  0'47  inch  centre  to 
centre.  The  mild  steel  wire  in  the  spiral  had  a  diameter  of  O'HS  inch  and  a 
pitch  of  1'18  inches.  Ten  wires  were  jointed  in  the  member,  the  junction  consist- 
ing of  an  overlap  of  11 '8  inches,  the  free  ends  being  bound  with  soft  iron  wire. 
The  junctions  were -spread  over  the  length  of  the  member.  The  reinforcing  wires, 
which  extended  beyond  the  end  of  the  concrete  casing,  were  gathered  together  and 
fixed  into  a  steel  cage  with  spelter,  there  being  a  clear  distance  about  17  inches 
between  the  end  of  the  concrete  casing  and  the  near  face  of  the  metallic  anchor  block. 
The  concrete  casing  had  a  square  section  of  3-15  inches  side. 


TESTS   OF   TENSION   MEMBERS 


67 


—    3-IS" 

FIG.  26. 


Member  No.  2  was  of  similar  design,  but  was  moulded  under  a  tension  of 
S'9  tons  per  square  inch  of  the  area  of  the  reinforcement,  which  was  maintained 
up  to  the  moment  of  the  test.  The  longitudinal 
wires  were  OH 8  inch  diameter,  giving  a  per- 
centage reinforcement  of  3*4.  The  mild  steel  wire 
constituting  the  spiralling  had  a  diameter  of 
0-079  inch  and  a  pitch  of  about  half  an  inch. 
Five  of  the  wires  were  in  two  parts,  the  junctions 
being  formed  by  means  of  a  muff  consisting  of  a 
slightly  flattened  steel  tube  2  inches  long,  through 
which  the  ends  of  the  wires  were  passed  and  allowed 
to  project  for  lengths  of  9  inches  beyond  the  muff. 
The  free  ends  of  the  wires  were  in  this  case  moulded 
into  a  concrete  head. 

The  longitudinal  reinforcements  consisted  of  a 
specially  hard  steel,  which  had  a  limit  of  elasticity 
in  the  neighbourhood  of  its  breaking  strength.  The 

mean  resistance  to  tension  for  wires  of   0'177  inch  diameter  was    107  tons  per 
square  inch,  and  for  wires  of  0'118  inch  diameter  was  115  tons  per  square  inch. 

The  cement  was  Portland  cement  of  French  manufacture.  Its  setting  time  was 
4J  hours.  Its  resistance  to  tension  after  seven  days  was  620  Ibs.  per  square  inch,  and 
after  twenty- eight  days  734  Ibs.  per  square  inch.  The  mortar  consisted  of  four  parts  of 
this  cement  to  five  parts  by  measure  of  fine  siliceous  sand  passing  through  a  sieve  with 
holes  0'039  inch  diameter  and  without  much  dust.  The  division  between  the 
mortar  and  the  pure  cement  was  maintained  by  a  sheet-brass  diaphragm  0*394  inch 
thick,  with  holes  to  keep  the  wires  at  the  proper  spacings. 

Tension  was  applied  to  the  member  by  means  of  the  head  of  metal  in  one  case 
and  of  concrete  in  the  other. 

Member  No.  1  was  tested  after  a  hardening  of  one  month.  This  member  had 
several  cracks  in  the  part  made  of  pure  cement ;  none  were  visible  in  the  part  in 
mortar.  In  consequence  of  the  difference  of  inclination  of  the  reinforcing  wires 
between  the  member  and  the  fixed  head  the  distribution  of  the  load  was  necessarily 
very  uneven,  with  the  result  that  the  wires  began  to  break  one  after  the  other  at  a 
stress  of  7 4 '3  tons  per  square  inch,  calculated  as  being  uniformly  spread  over  the 
reinforcement.  The  first  fissure  in  the  mortar  appeared  at  a  stress  of  10 '7  tons  per 
square  inch  of  the  reinforcement,  assuming  the  load  uniformly  distributed. 

Member  No.  2  was  tested  after  a  hardening  of  three  months.  At  the  time  of  the 
test  only  two  small  cracks  near  the  extremity  in  the  pure  cement  were  visible.  The 
first  crack  in  the  pure  cement  occurred  when  a  stress  of  15*5  tons  per  square  inch 
of  the  reinforcement  had  been  applied,  and  the  first  fissure  in  the  mortar  when  that 
stress  was  increased  to  24  tons  per  square  inch.  The  tension  was  not  carried 
beyond  43  tons  per  square  inch  of  the  reinforcement.  At  that  stress  the  mortar 
and  cement  were  cracked  at  right  angles  to  the  reinforcement  every  4  inches  or  so. 


P  2 


CHAPTER  V 
THE  REPORT  AND  DRAFT  REGULATIONS  PRESENTED  BY  THE  COMMISSION 

THE  Commission  arranged  its  work  in  the  following  manner : — 

1.  It  set  out  to  define  as  precisely  as  possible  the  materials  constituting  rein- 
forced concrete,  the  principal  conditions  they  ought  to  fulfil,  and  the  indispensable 
precautions  to  be  taken  in  construction. 

2.  It  studied  the  elementary  properties  of  the  materials,  taken  separately  and 
also  associated. 

3.  The  physical  and  elastic  properties  thus  determined  were  examined  to  find,  if 
possible,  a  rational  basis  for  and  a  scientific  method  of  calculation. 

4.  The  results  obtained  from  these  processes  were  compared  with  successful 
practice. 

The  Report  passes  in  review  the  principal  results  obtained  from  the  experimental 
work  of  the  Commission. 

Variations  in  Volume  Resulting  from  the  Setting  of  Cement. 

It  is  known  that,  extending  over  some  months,  mortars  and  concretes  exposed  to 
air  undergo  contraction  during  setting,  which  is  greater  the  higher  the  proportion  of 
cement.  This  contraction  leads  to  internal  stresses,  tension  in  the  concrete  and 
compression  in  the  reinforcement.  When  this  contraction  is  opposed  by  external 
connections,  serious  cracking  frequently  results. 

The  concrete  employed  in  the  tests  was  of  the  proportion  most  frequently 
employed  in  open-air  work  in  France — viz.,  6  cwts.  Portland  cement,  28 '7  cubic 
feet  of  gravel  and  14'4  cubic  feet  of  sand,  which,  when  rammed  into  the  work,  give 
about  36  cubic  feet  of  concrete,  or  about  1^  cubic  yards. 

Although  the  contraction  varies  somewhat  with  the  length  and  section  of  the 
member,  the  Commission  put  it  at  0'025  per  cent,  when  it  is  exposed  to  the 
weather  immediately  after  manufacture,  and  0'020  per  cent,  when  it  is  maintained 
humid  for  the  first  three  weeks. 

The  Commission  did  not  insist  that  the  contraction  should  be  taken  account  of, 
except  in  long  members. 

Thermal  Variations  of  Volume. 

No  new  experiments  were  made  on  this  subject,  tjut  it  appeared  from  the 
collected  results  of  previous  experiments  that  a  coefficient  of  expansion  per 
100  degrees  Centigrade  of  0*0011,  or  (HI  per  cent.  (0-00061  per  100  degrees 
Fahrenheit),  might  'without  sensible  error  be  adopted,  and  that  the  coefficients  of 
expansion  of  concrete  and  steel  might  be  taken  as  equal. 

From  measurements  made  on  an  arched  bridge  at  Chatelherault,  it  was  demon- 
strated that  reinforced  concrete  structures  are  only  very  slightly  sensible  to  hourly 
variations  of  temperature,  but  that  they  assume  the  mean  daily  temperature. 


RESISTANCE   TO   CRUSHING  69 

Resistance  and  Deformation  of  Concrete  Submitted  to  Tension. 

When  concrete,  not  reinforced,  is  submitted  to  simple  tension,  the  tension 
increases  proportionally  to  the  elongation  until  rupture  is  produced  for  an 
elongation  of  at  least,  in  general,  O'Ol  per  cent. 

When  concrete,  not  reinforced,  is  submitted  to  bending,  the  part  in  tension 
has  a  certain  ductility.  From  a  limit  which  appears  very  near  the  maximum 
elongation  when  submitted  to  simple  tension,  the  modulus  of  elasticity  of  the 
concrete  in  the  tension  part  of  the  beam  diminishes  very  markedly,  and 
rupture  is  produced  for  an  elongation  which  generally  lies  between  O'Ol  and 
0-02  per  cent. 

Concrete  properly  prepared  and  reinforced  becomes  much  more  ductile  still. 
From  the  experiments  of  the  Commission  it  was  established  that  the  elongation 
of  the  concrete  before  rupture  went  up  to  O135  per  cent.,  and  it  was  observed 
that  until  an  elongation  between  O'Ol  and  0'02  per  cent,  was  reached,  the 
concrete  had  practically  the  same  modulus  of  elasticity  as  concrete  not  reinforced. 
Beyond  this  limit  the  modulus  of  elasticity  is  sensibly  zero ;  or,  in  other  words, 
whilst  the  elongation  increases,  the  tension  of  the  concrete  remains  very  nearly 
constant  and  in  the  neighbourhood  of  the  resistance  of  concrete  not  reinforced. 

Resistance  to  Crushing. 

Table  No.  22,  pp.  70 — -73,  contains  a  resume  of  the  results  of  the  experi- 
ments made  by  the  Commission  and  of  those  made  by  Professor  Bach  of  Stuttgart. 

In  the  first  six  divisions  the  particulars  characterising  each  series  of  experiments 
are  indicated.  In  division  7  is  given  the  increase  of  resistance  in  Ibs.  per  square 
inch  of  total  section  which  the  reinforcement  has  produced.  The  figure  relative 
to  each  column  was  found  by  deducting  from  its  resistance  that  of  a  test  column 
not  reinforced  and  made  of  the  same  concrete. 

To  permit  of  the  comparison  of  the  different  types  of  reinforcement,  a  common 
measure  has  been  devised  for  them  as  follows  : — 

Suppose  the  column  to  be  reinforced  with  an  equivalent  bar  having  the  same 
total  volume  as  all  the  reinforcements  of  whatever  kind  in  the  column.  Divide 
the  total  increase  of  resistance  by  the  area  of  this  equivalent  bar.  The  quotient 
will  represent  the  increase  of  resistance  of  the  concrete  produced  by  each  square 
inch  of  reinforcement. 

The  figures  given  in  Table  No.  22  call  for  the  following  remarks  : — 

In  Series  A,  in  order  to  study  the  slipping  of  the  reinforcements,  the  concrete 
covering  the  ends  of  the  longitudinal  bars  was  removed.  As  a  result,  the  resistance 
to  crushing  has  been  almost  exactly  the  same,  although  the  percentage  of  metal 
varied  from  0*28  to  3'97  per  cent. 

In  Series  B,  prepared  conformably  to  the  programme  of  the  Society  of  German 
Reinforced  Concrete  Engineers,  the  ends  of  the  longitudinal  bars  were  2  inches 
from  the  ends  of  the  columns  and  left  buried  in  the  concrete.  The  resistance  per 
square  inch  of  the  equivalent  bars  in  these  cases  varied  from  6 -6 7  to  12 '3 3  tons 
per  square  inch,  the  former  figure  being  that  corresponding  to  the  large  longitudinal 
bars  with  the  interties  spaced  widely  apart,  the  latter  to  small  bars  with  more  closely 
spaced  interties. 

Experiments  A  and  B  having  drawn  attention  to  the  importance  of  the  end 
conditions  of  the  longitudinal  bars,  there  was  realised  in  Series  C  the  most  perfect 
arrangement  from  this  point  of  view.  The  bars  were  cut  square,  and  adjusted  to 


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74  REINFORCED   CONCRETE 

bear  exactly  on  the  heads  of  the  testing  machine.  The  columns  of  this  series,  which 
were  made  with  the  minimum  quantity  of  water  necessary,  have  shown  an  increase 
of  strength  of  15-25  tons  per  square  inch  of  the  equivalent  bar,  whilst  those  made 
by  pouring  the  fluid  concrete  into  the  mould  only  showed  an  increase  of  5 '9 7  tons 
per  square  inch  at  the  end  of  twenty-eight  days. 

In  the  tests  of  Series  D,  the  columns  were  6'56  feet  and  13-12  feet  in  length. 
Great  differences  of  resistance  were  found  in  the  non -reinforced  columns  of  these 
lengths.1  This  fact  diminishes  the  confidence  one  might  have  in  the  results  of 
this  series,  and  explains  to  some  extent  how  identical  reinforcements  have  given 
augmentations  of  resistance  of  6 '4  and  19 '8  tons  per  square  inch  in  columns  which 
only  differ  by  the  proportions  of  the  concrete.  There  is  reason  to  set  aside  these 
extreme  values. 

All  the  columns  of  the  first  four  series  crushed  without  notable  flexion. 

The  columns  fulfilling  the  conditions  which  the  Commission  judged  necessary 
to  assure  the  efficiency  of  the  spiralling  have  given  the  results  B',  C'  and  D', 
which  correspond  to  the  Series  B,  C  and  D  of  the  columns  reinforced  with  intertied 
longitudinal  bars. 

The  columns  of  Series  B'  were  made  with  little  care  in  order  to  determine  the 
minimum  resistance  one  might  obtain  on  works.  For  example,  the  spacing  of  the 
spirals  from  centre  to  centre  has  varied  from  half  an  inch  to  3  inches  in  one  single 
piece,  and  the  longitudinal  bars  from  1§  inches  to  5  inches. 

In  Series  C'  it  should  be  noticed   that  the  spiralling  has  given  to  concrete 

1  The  non-reinforced  columns  of  6'56  and  13'12  feet  long  were  made  at  the  same  time  as  the 
columns  of  Series  D  and  D'  to  serve  as  references.  They  were  formed  of  the  same  concrete,  and 
were  rammed  with  the  same  care.  Their  resistance  to  crushing  without  buckling  was  for 
concrete  containing 

7  cwts.  cement    3,440  Ibs.  per  square  inch  for  columns    6*56  feet  long. 
2,820  do.  do.  13'12      do. 

Difference      620  Ibs.  per  square  inch. 

10  cwts.  cement    2,630  Ibs.  per  square  inch  for  columns    6-56  feet  long. 
2,090  do.  do.  13-12      do. 


540  Ibs.  per  square  inch. 

To  determine  the  cause  of  the  differences  of  resistance  of  the  columns  6'56  and  13'12  feet  long 
pieces  were  cut  from  the  top  and  the  base  of  each  of  the  columns,  and  it  was  found  that  the 
resistance  of  the  base  of  each  column  exceeded  that  of  the  upper  part  by  1,365  and  2,620  Ibs.  per 
square  inch  for  concrete  containing  7  cwts.  and  10  cwts.  of  cement  respectively. 

The  explanation  of  these  facts  appears  to  be  the  following.  The  concrete  gives  up  during 
the  ramming  and  up  till  the  commencement  of  setting  part  of  the  excess  of  water,  which  must 
in  every  case  be  added  to  facilitate  the  placing  of  the  concrete.  The  water  which  thus  comes  from 
the  lower  beds  adds  itself  in  the  concrete  superposed  to  that  which  the  latter  contains.  Thus  the 
higher  up  one  goes  in  the  column  the  wetter  is  the  concrete,  with  the  above-mentioned  result. 
The  effect  is  the  more  marked  the  richer  the  concrete  in  cement.  For  the  interpretation  of  the 
results  of  the  experiments  of  Series  D',  which  included  columns  7'55,  8'53  and  9'84  feet  long, 
it  was  observed  that  the  resistance  of  the  concrete  in  these  cases  varied  according  to  a  linear 
law  between  the  resistances  observed  for  the  concrete  of  6-56  feet  and  13*12  feet. 

It  is  important  to  point  out  that  in  order  to  maintain  a  uniform  quality  throughout  the  whole 
height  of  columns  it  is  necessary  to  employ  drier  concrete  as  the  work  ascends,  and  it  is  impor- 
tant to  dispose  the  reinforcements  in  such  a  way  as  to  permit  of  the  employment  of  concrete 
gauged  without  excess  of  water. 

These  facts  show  how  difficult  is  the  comparison  of  reinforced  pieces  of  different  types  and 
of  the  unreinforced  pieces  of  the  same  type  cast  for  comparison  of  the  strength  of  the  concrete. 
Pieces  to  be  compared  should  have  dimensions  such  that  the  final  degree  of  humidity  of  the 
concrete  is  the  same. 

These  facts  explain  the  contradictions  existing  in  experiments  apparently  comparable,  and 
lead  one  to  take  account  not  of  the  isolated  anomalies,  but  only  of  the  main  lines  of  the  results 
of  experiments. 


RESISTANCE   TO   CRUSHING  75 

poured  without  ramming  and  tested  after  twenty-eight  days  the  same  increase  of 
resistance  as  concrete  rammed  with  care. 

The  columns  of  Series  D'  were  prepared  to  study  the  resistance  to  buckling. 
Setting  aside  those  indicated  as  having  buckled  without  crushing,  the  others  show 
an  increase  of  crushing  resistance,  per  square  inch  of  the  cross  sectional  area  of  the 
equivalent  bar  having  the  same  volume  as  the  longitudinals  and  spirals  together, 
of  28-5  tons  to  40  tons. 

A  number  of  columns  tested  at  Stuttgart  did  not  fulfil  the  conditions  necessary 
to  give  to  the  spiralling  the  proper  efficiency.  In  one  case  the  longitudinal 
reinforcements  were  too  feeble,  in  the  other  the  pitch  of  the  spirals  was  too  great. 
The  results  show  analogous  increases  to  those  of  columns  reinforced  with  longitudinal 
intertied  bars.  These  experiments  thus  establish  a  transition  between  the  two 
types  of  reinforcement.  The  following  description  of  the  test  of  a  strongly 
spiralled  column,  which  consequently  presents  features  highly  characteristic  of  this 
type  of  reinforcement,  is  given  to  enable  a  clear  idea  to  be  formed  of  the  phenomena 
met  with  during  the  loading  to  destruction  of  such  a  column. 

The  column  was  6 '56  feet  long,  composed  of  concrete  containing  7  cwts.  of 
cement  and  reinforced  to  a  total  percentage  of  4  -91.  The  first  fissures  in  the 
concrete  covering  the  spirals  were  apparent  when  the  pressure  had  attained 
4,370  Ibs.  per  square  inch  of  the  total  section.  The  pressure  was  increased  to 
a  maximum  of  7,050  Ibs.  per  square  inch,  when  buckling  commenced.  The 
loading  was  maintained  until  the  moment  when  the  deflection  attained  a  value 
of  4  inches,  the  load  at  this  time  corresponding  to  a  stress  of  4,240  Ibs. 
per  square  inch  of  the  spiralled  core,  the  external  envelope  of  concrete  over 
the  spirals  having  by  this  time  almost  entirely  disappeared.  In  the  column  thus 
bent  there  was  no  trace  of  crushing  of^  the  spiralled  core,  but  in  the  parts  of 
greatest  curvature  radial  tension  fissures  were  observed  tending  to  cut  the  concrete 
in  slices. 

In  columns  which  have  crushed  without  bending,  the  failure  of  the  column  is 
produced  sometimes  by  the  thinning  out  and  rupture  of  a  spiral,  sometimes  by  the 
shearing  of  the  concrete  on  oblique  planes. 

Both  in  the  columns  which  failed  by  flexion  and  those  which  ruptured,  the 
concrete  of  the  core  away  from  the  vicinity  of  the  rupture  presented  no  traces  of 
alteration.  This  was  demonstrated  by  cutting  out  test  prisms  from  the  cores  of 
columns  which  had  resisted  high  pressures.  For  example,  crushing  resistances  of 
3,930  and  2,470  Ibs.  per  square  inch  were  obtained  from  prisms  cut  from  the  base 
and  the  top  respectively  of  a  column  containing  7  cwts.  Portland  cement  and 
reinforced  to  6*34  per  cent.,  and  which  had  resisted  a  pressure  of  9,080  Ibs.  per 
square  inch  of  the  spiralled  core.  A  column  reinforced  to  4'91  per  cent.,  which 
had  resisted  a  pressure  of  8,740  Ibs.  per  square  inch,  gave  corresponding  resistances 
of  2,260  and  2,030  Ibs.  per  square  inch  respectively. 

These  facts  indicate  that  cracking  takes  place  prematurely  in  the  outer  cylinder 
of  concrete  covering  the  spirals,  but  that  that  does  not  compromise  the  solidity 
of  the  core  on  which  the  resistance  to  crushing  depends.  Such  cracking  must, 
nevertheless,  be  avoided  in  practice. 

The  experiments  of  Series  D  showed  that,  on  the  average,  the  pressure  under 
which  the  first  fissures  appeared  exceeded  by  about  940  Ibs.  per  square  inch  the 
resistance  of  the  non-reinforced  columns,  and  that  the  excess  resistance  was 
almost  the  same  for  short  columns  reinforced  to  nearly  5  per  cent.,  and  for 
long  columns  only  reinforced  to  2  per  cent.  The  pressures  which  spiralled 
pieces  can  resist  without  sustaining  any  damage  whatever  depends  thus  on  the 


76  REINFORCED   CONCRETE 

inherent  resistance  of  the  concrete,  and  is  but  little  augmented  with  the  percentage 
of  metal. 

In  the  experiments  at  Stuttgart,  the  results  point  to  the  same  conclusions.  In 
that  case  the  resistance  at  which  cracking  of  the  envelope  of  the  spirals  took  place 
exceeded  by  about  1,400  Ibs.  the  resistance  of  the  non-reinforced  columns. 

It  may  safely  be  allowed  that  in  ordinary  concrete,  containing  6  cwt.  of  cement, 
for  which  a  resistance  of  2,280  Ibs.  per  square  inch  may  be  reckoned  on,  the  load 
which  causes  cracking  in  spiralled  members  is  2,850  Ibs.  per  square  inch.  In 
members  thus  proportioned  the  pressure  might  thus  be  limited  to  1,440  Ibs.  per 
square  inch;  that  is,  to  62  per  cent,  of  the  inherent  resistance  of  the  concrete,  no 
matter  how  high  the  percentage  reinforcement  might  be. 

The  pressure  being  thus  limited  to  1,440  Ibs.  per  square  inch  for  concretes  of 
middling  quality,  and  to  1,600  or  1,700  Ibs.  per  square  inch  at  the  most  for  concretes 
of  the  best  quality,  and  on  the  other  hand,  the  coefficient  of  security  3,  4  or  5  being 
applied  as  regards  crushing  or  buckling  phenomena,  it  is  evident  that  there  is  no  reason 
for  increasing  the  percentage  of  metal  beyond  that  necessary  to  obtain  resistances  of 
4,800  to  8,500  Ibs.  per  square  inch.  For  this  reason  the  experiments  made  at  the 
Laboratory  of  the  Ecole  des  Fonts  et  Chaussees  on  cylinders  very  strongly  spiralled, 
in  which  resistances  up  to  25, 600  Ibs.  per  square  inch  were  obtained,  have  not  been 
described.  These  experiments,  however,  show  that  the  useful  effect  of  spiralling 
extends  to  very  wide  limits. 

When  compression  tests  on  concrete  are  made,  creaking  noises  proceed  from  the 
concrete  when  the  stress  reaches  a  value  which  varies  within  somewhat  wide  limits. 
In  the  non-reinforced  columns  of  Series  D  noises  were  heard,  sometimes  near  the 
crushing  load,  sometimes  when  the  stresses  were  less  than  720  Ibs.  per  square  inch. 
In  spiralled  and  longitudinally  reinforced  pieces  the  first  noises  were  heard  sometimes 
when  the  stress  was  in  the  neighbourhood  of  the  crushing  strength  of  ordinary 
concrete,  sometimes  when  that  figure  had  been  exceeded  by  700  Ibs.  per  square  inch. 
The  cause  of  these  noises  is  not  known,  but  it  is  noticed  that  they  precede  but  slightly 
the  crushing  of  non-reinforced  or  longitudinally  reinforced  columns,  and  the  cracking 
of  the  envelope  in  spirally  reinforced  columns.  It  is  thus  possible  that  these  noises 
indicate  to  the  ear  the  commencement  of  processes  which  are  not  visible  to 
the  eye. 

The  great  ductility  of  spiralled  concrete  is  another  phenomenon  which  falls  to  be 
recorded.  In  short  pieces,  in  which  sensible  uniformity  of  quality  might  be  looked 
for,  the  shortening  observed  was  from  1  to  3*6  per  cent,  of  the  original  length.  In 
longer  pieces,  where  there  is  considerable  variation  from  the  top  to  the  bottom,  the 
shortening  measured  at  the  middle  of  the  length  has  varied  from  0'5  to  0*75  per 
cent,  in  columns  6  feet  long,  and  from  0*3  to  0'4  per  cent,  in  longer  columns.  The 
upper  part,  which  had  the  least  resistance,  yielded  before  the  concrete  elsewhere  had 
resisted  the  maximum  load,  and  therefore  the  maximum  deformation  of  which  it  was 
capable.  The  considerable  bending  observed  in  spiralled  pieces  is  another  proof  of 
the  ductility  of  concrete  reinforced  in  this  way. 

Pitch  of  Spirals. 

The  network  of  spirals  and  longitudinal  reinforcements  which  constitutes  the 
cage  is  intended  to  prevent  the  transverse  swelling  of  the  concrete  under  the  load. 
It  opposes  the  escape  of  material  between  the  meshes,  and  these  ought  evidently  to 
be  the  closer,  the  greater  the  load  designed  for.  Only  experience  can  dictate  the 
proper  arrangement  from  this  point  of  view. 


MODULUS    OF   ELASTICITY  77 

In  the  Stuttgart  experiments  the  spacing  centre  to  centre  of  the  spirals  was  from 
—  to  —  in  columns  which  gave  medium  results,  and  —  in  those  in  which  the 

resistances  were  conformable  to  the  draft  provisions  of  the  Commission,  d  being  the 
diameter  of  the  circle  inscribed  in  the  octagon  forming  the  transverse  section  of  the 
column. 

The  feebly  spiralled  columns  tried  with  success  by  Professor  Guidi  at  Turin  had 

the  spirals  spaced  at  — . 
o 

In  the  columns  of  Series  D  good  results  were  obtained  with  a  spacing  of  the  spirals 

of  —  for  greater  resistances,  and  — -  for  less. 
8  4'4 

The  Commission  recommended  that  the  pitch  of  the  spirals  be  not  unduly 
diminished,  owing  to  the  difficulty  occasioned  thereby  of  ramming  the  concrete. 

As  all  the  experiments  point  to  the  ramming  having  a  considerable  influence  on 
the  mechanical  qualities  of  the  concrete,  it  is  suggested  that  the  efficiency  of  the 
network  preventing  lateral  spreading  should  be  increased  for  increasing  loads  by 
augmenting  the  section  of  the  longitudinal  rods  rather  than  by  decreasing  the  pitch 
of  the  spirals. 

Elasticity. 

The  irregularity  of  concrete  is  still  greater  from  the  point  of  view  of  elasticity 
than  from  that  of  resistance.  From  a  concrete  composed  of  6  cwts.  Portland 
cement,  14*35  cubic  feet  of  sand,  and  28*70  cubic  feet  of  gravel  the  Commission 
has  obtained  moduli  of  elasticity  under  a  light  load  varying  from  2-28  X  106 
to  5 '6 9  X  106  Ibs.  per  inch2,  according  to  the  quantity  of  water  used  in  gauging  and 
the  method  of  ramming. 

The  modulus  of  non-reinforced  concrete  diminishes  as  the  load  increases, 
especially  beyond  a  limit  in  the  neighbourhood  of  one-half  or  two-thirds  of  the 
crushing  load,  and  it  is  necessary,  having  regard  to  buckling,  to  take  into  considera- 
tion the  modulus  under  pressures  superior  to  the  working  load.  Consequently,  a 
modulus  of  elasticity  of  2,130,000  Ibs.  per  square  inch,  or  950  tons  per  square  inch, 
may  be  properly  allowed. 

This  irregularity  in  non-reinforced  concrete  necessarily  shows  itself  in  the  tests 
of  reinforced  columns. 

In  Series  A,  the  non-reinforced  column  had  not  the  same  dimensions  as  the 
reinforced  one,  and  the  results  of  this  series  cannot  be  compared.  Only  the  columns 
of  15-75  inch  side,  in  which  the  percentage  varied  from  0'28  per  cent,  to  3*97  per 
cent.,  are  suitable  for  purposes  of  comparison. 

There  has  been  calculated  the  total  resistance  per  square  inch  which  the 
different  columns  gave  when  their  shortenings  had  the  same  value  of  0'02  per  cent. 
In  order  to  compare  two  columns  the  differences  of  their  unital  resistances  has 
been  divided  by  the  shortening  for  which  the  comparison  was  made,  and  by  the 
difference  in  the  unital  reinforcement.1  The  quotient  gives  a  measure  of  the 
useful  elastic  effect  of  the  excess  of  reinforcement  in  the  more  heavily  reinforced 
column,  and  it  ought,  hypothetically,  for  average  quality  of  steel  to  be  about 
29,100,000  Ibs.  per  inch2,  or  13,000  tons  per  inch2  if  the  reinforced  columns  were 
formed  of  identical  materials  simply  associated  in  a  common  shortening. 

1  The  unital  reinforcement  is  the  area  of  equivalent  reinforcement  per  unit  area  of  column 
or  the  percentage  reinforcement  -r-  100. 


78  REINFOKCED   CONCRETE 

On  comparing  the  columns  reinforced  to  3*97  per  cent,  and  0-28  per  cent, 
respectively,  an  apparent  modulus  of  elasticity  of  1,710,000  Ibs.  per  inch2,  or 
7,600  tons  per  inch2,  was  found  for  the  metal  in  excess  of  0*28  per  cent. 

In  Series  C  and  D  similar  calculations  give  the  apparent  modulus  of  elasticity 
of  the  metal  as  varying  from  17,100,000  Ibs.  per  inch2,  or  7,600  tons  per  inch2,  to 
10,000,000  Ibs.  per  inch2,  or  4,400  tons  per  inch.2 

It  was  found  experimentally  in  series  A,  that  except  in  the  neighbourhood 
of  the  ends,  relative  slipping  of  the  concrete  and  steel  was  absolutely  negligible. 

These  facts  lead  to  the  conclusion  that  since  the  metal  does  not  slip  and  in 
consequence  sustains  the  same  shortening  as  the  surrounding  concrete,  it  certainly 
furnishes  resistances  corresponding  to  its  modulus  of  elasticity.  Its  apparent  effect 
having  been  much  less,  we  are  led  to  conclude  that  the  modulus  of  elasticity  of  the 
concrete  has  been  less  in  the  reinforced  columns  in  question  than  in  those  not 
reinforced.  This  weakness  in  the  concrete  might  be  due  to  three  possible  causes  : 
either  an  increase  in  the  quantity  of  water  used  in  mixing  the  concrete,  owing  to  the 
greater  ease  of  working  it  in  the  moulds,  or  the  less  perfection  of  ramming  owing  to 
the  constraint  of  the  reinforcements,  or  owing  to  the  prevention  by  the  reinforce- 
ments of  the  full  contraction  of  the  concrete  during  its  setting,  and  which,  perhaps, 
will  hinder  it  from  acquiring  all  the  mechanical  qualities  of  which  it  is  capable. 

The  first  cause  suggested  did  not  operate  in  any  of  the  experiments  made  by 
the  Commission,  because  the  quantity  of  water  used  was  weighed  with  care,  and  the 
second  did  not  affect  the  columns  of  Series  A,  as  these  were  all  similar. 

Whilst  the  experiments  of  the  Commission  and  also  those  of  Professor  Guidi  at 
Turin  gave  results  for  the  elasticity  of  the  metal  inferior  to  that  indicated  by  the 
theory  of  elasticity,  the  experiments  of  Professor  Bach  at  Stuttgart,  under  the 
auspices  of  the  Society  of  German  Reinforced  Concrete  Engineers,  gave  results  for 
the  moduli  of  elasticity  of  longitudinal  reinforcements  corresponding  sensibly  to  the 
figures  deduced  from  theory. 

All  that  may  be  affirmed  regarding  the  elasticity  of  pieces  longitudinally 
reinforced  is  that  in  careful  experiments  the  apparent  elastic  effect  of  the  longitu- 
dinal bars  has  varied  from  less  than  half  the  value  indicated  by  the  theory  of 
elasticity  to  values  sensibly  equal  to  that  value.  Under  these  conditions  it 
seemed  reasonable  to  adopt  the  simplest  solution,  which  consists  in  allowing  from 
the  point  of  view  of  elasticity  the  coefficient  of  equivalence  between  the  metal  and 
the  concrete  which  were  adopted  from  the  point  of  view  of  resistance  to  crushing. 
These  coefficients  vary  from  8  to  15,  combined  with  a  modulus  of  elasticity 
2,130,000  Ibs.  per  square  inch,  or  952  tons  per  square  inch ;  they  attribute  to  the 
metal  values  of  the  modulus  of  elasticity  varying  apparently  from  7,616  tons  per 
inch2  to  14,280  tons  per  square  inch,  which  agree  with  the  results  obtained 
at  Paris,  Stuttgart,  and  Turin. 

The  causes  indicated  above  that  diminish  the  coefficient  of  elasticity  act  in  the 
same  sense  on  the  resistance  of  concrete  to  crushing. 

The  Commission  decided  that  whilst  awaiting  further  experiments  on  the 
effect  of  transverse  reinforcement  or  spiralling  on  the  elasticity  of  concrete,  it  is 
prudent  to  entirely  neglect  any  increase  which  such  reinforcement  might  give. 

Deformation  of  Plane  Sections  in  Bending. 

Although  not  rigorously  exact,  the  hypothesis  of  the  conservation  of  plane 
sections  serves  as  a  rational  basis  to  the  theory  of  resistance  of  homogeneous 
materials.  Its  application  to  a  heterogeneous  material  such  as  reinforced  concrete 


BENDING   PHENOMENA  79 

a  priori^  open  to  serious  doubt.  One  might  readily  understand  that  the  slipping 
of  the  reinforcements  and  the  cracking  of  the  concrete  in  tension  would  make  the 
hypothesis  entirely  unworkable. 

A  very  great  number  of  experiments  made  on  the  beams  7*87  inches  X 
15*75  inches,  and  13' 12  feet  span,  have  proved  that  sections  originally  plane  remain 
sensibly  so  during  bending,  except  in  the  immediate  neighbourhood  of  the  supports 
and  of  the  points  of  application  of  heavy  concentrated  loads. 

Away  from  these  exceptional  points,  where  in  actual  structures  it  might  be 
useful  to  consider  specially  the  strength  from  the  point  of  view  of  local  stresses, 
the  warping  of  sections  originally  plane  does  not  modify  notably  the  longitudinal 
deformations,  which  serve  as  a  basis  for  the  calculation  of  deflected  pieces.  Any 
deviation  from  the  hypothesis  of  the  conservation  of  plane  sections  may  thus, 
without  sensible  error  in  the  calculation  of  tensions  or  compressions,  be  neglected. 

Application  of  the  Laws  of  Simple  Deformations  to  the  Calculations  of  Bent 

Pieces. 

In  the  theory  of  bending  of  homogeneous  materials,  it  is  allowed  that  to  a 
certain  longitudinal  elongation  or  contraction  there  corresponds  a  certain  tension 
or  compression  in  bending  and  also  in  traction  or  thrust. 

To  discover  to  what  extent  this  assumption  is  applicable  to  reinforced  concrete, 
the  following  investigations  were  carried  out: — 

A  number  of  prisms  were  made  simultaneously  with  the  beams  of  7*87  inches  X 
15*75  inches  section,  and  13*12  feet  span,  and  the  moduli  of  elasticity  of  the 
concrete  and  the  reinforcements  respectively  were  measured.  Applying  with  these 
figures  the  above  hypothesis,  there  was  determined  by  calculation  the  position  of 
the  neutral  axis,  in  the  period  of  deformation  after  the  limit  of  elasticity  of  the 
stretched  concrete  had  been  passed  ;  that  is,  in  the  period  in  which  the  tension  of 
the  elongated  concrete  ought  to  be  constant.  Results  were  found  almost  rigorously 
to  conform  to  those  given  by  actual  measurement  during  experiment. 

It  has  been  concluded  that  the  hypothesis  in  question  might,  concurrently  with 
the  hypothesis  of  the  conservation  of  plane  sections  during  bending,  be  safely 
applied  in  calculation,  assuming  at  the  same  time  that  the  laws  of  deformation  by 
tension  or  thrust  are  those  already  formulated. 

Adhesion  of  the  Concrete  to  the  Metal. 

For  simple  tension  or  compression  on  isolated  bars  imbedded  in  concrete  the 
Commission  found  values  of  the  resistance  to  unbedding  of  from  97  to  420  Ibs.  per 
square  inch  of  the  surface  of  contact.  For  bars  surrounded  by  spirals  or  placed 
in  the  folds  of  perpendicular  stirrups,  these  figures  varied  from  225  to  560  Ibs.  per 
square  inch. 

These  figures  give  no  indication,  however,  of  the  tendency  to  slip  in  members 
where  bending  imposes  other  stresses  on  the  member.  For  this  information,  beams 
in  which  failure  took  place  by  slipping  of  the  reinforcements  were  studied,  and  in 
doing  so  it  was  assumed,  according  to  the  usual  hypothesis  conform  to  the  theory  of 
perfectly  elastic  bodies,  that  the  slipping  stress  varied  with  the  shearing  stress. 
Consequently  the  resistance  to  slipping  furnished  by  the  ends  of  the  longitudinal 
reinforcement,  which  projected  beyond  the  supports,  was  neglected,  since  there  is 
no  shearing  force  there.  The  values  of  the  adhesion  thus  found  varied  from  185 
to  213  Ibs.  per  square  inch.  Other  experimenters  applying  the  same  mode  of 
calculation  have  found  similar  values. 


80  REINFORCED   CONCRETE 

Resistance  to  Shearing  Forces. 

The  experiments  indicate  that  whilst  vertical  stirrups  are  useful  in  a  beam  just 
before  the  formation  of  cracks  and  after  cracks  have  formed,  stirrups  inclined  in  the 
direction  of  the  tension,  or  longitudinal  reinforcing  bars  bent  upwards  towards  the 
supports,  give  much  more  help  to  the  concrete  under  working  loads. 

Beams  which  were  reinforced  in  both  tension  and  compression  areas,  and  which 
had  no  stirrups,  continued  to  support  a  load  in  virtue  of  the  resistance  of  the 
reinforcements  after  the  concrete  had  fissured  for  J  of  its  full  depth  in  the  part 
exposed  to  shear.  The  resistance  of  the  reinforcements  to  the  shearing  forces  was 
probably  aided  by  a  kind  of  frictional  resistance  in  the  compression  area  of  the 
beam. 

Experiments  on  the  Eesistance  and  Deformation  of  Works  Constructed  for  the 

Exhibition  of  1900. 

Experiments  were  made  under  the  direction  of  M.  Rabut  on — 

1.  Two  floor  slabs. 

2.  A  ribbed  floor. 

3.  A  footbridge. 

4.  A  retaining  wall. 

These  structures  were  designed  by  the  Hennebique  empirical  formulae,  and 
constructed  according  to  the  usual  practice  of  that  firm.  The  experiments  were 
carried  out  to  determine — 

1°.  What  margin  of  security  might  be  relied  on. 

2°.  What  degree  of  solidarity  there  was  between  the  different  members. 

3°.  If  any  relation  could  be  determined  between  the  loads  and  the  deformations. 

On  the  first  point  the  experiments  showed  that  in  the  case  of  the  slabs  they 
carried  a  surcharge  equal  to  from  five  to  six  times  that  for  which  they  had  been 
designed.  The  ribbed  floor  supported  without  a  rupture  a  load  three  to  four 
times  greater  than  that  for  which  it  had  been  designed,  whilst  the  retaining  wall 
withstood  a  very  much  greater  load  than  that  which  ought  to  result  from  the  thrust 
of  the  earth. 

On  the  second  point  it  was  observed  that  concentrated  loads  were  distributed  not 
only  on  the  single  rib  on  which  they  rested,  but  sometimes  on  five  and  even  on  as 
many  as  seven. 

On  the  third  point,  although  a  precise  statement  of  the  relation  between  the 
deflections  and  the  stress  on  the  steel  or  concrete  has  not  been  possible,  the 
fact  that  the  deflections  under  growing  loads  follows  a  continuous  law,  in  spite  of 
the  formation  of  cracks,  was  clearly  demonstrated. 

Detailed  information  regarding  the  design  and  construction  of  these  structures, 
together  with  the  records  of  the  tests  and  the  analyses  of  the  results,  form  Part  I. 
of  the  French  edition  of  the  Report. 


CHAPTER  VI 

SOME  CONCLUSIONS  FROM  THE  STUDY  OF  THE  ELEMENTARY  PROPERTIES  OF  THE 
MATERIALS  CONSTITUTING  REINFORCED  CONCRETE 

Calculation  of  Stresses  and  Deformations. 

ONCE  the  hypothesis  of  the  conservation  of  plane  sections  is  accepted  with 
reference  to  reinforced  concrete  structures,  the  deformations  and  the  stresses  under 
any  loading  whatever  may  be  calculated  from  the  known  properties  of  the  com- 
ponents, but  in  every  case  the  calculation  is  a  complicated  one  and  frequently 
almost  insoluble. 

So  far  as  stresses  are  concerned,  the  tension  in  the  concrete  ought  to  be 
neglected,  which  leads  to  a  very  considerable  simplification  in  the  calculations,  and 
the  Commission  suggested  that  that  method  should  also  be  applied  to  the  calculation 
of  deformations.  The  deformations  thus  calculated  are  in  excess  of  those  to  be 
expected,  but  the  calculated  values  might  be  corrected  by  means  of  a  coefficient 
of  correction,  obtained  by  a  comparison  of  the  calculated  value  with  that  actually 
found  in  a  large  number  of  experiments.  Such  a  coefficient  would  be  a  function 
of  the  percentage  reinforcement. 

Coefficients  of  Security. 

The  Commission  were  of  opinion  that,  taking  into  account  the  excellent  protection 
afforded  to  the  metal  from  abrasion,  oxidation,  and  largely  from  shocks,  and  that 
in  well-designed  reinforcements  holes  and  grooves  are  avoided,  the  metal  may 
safely  be  stressed  by  working  loads  to  half  its  apparent  elastic  limit. 

The  risk  incurred  in  exceeding  the  limit  of  elasticity  is  twofold — viz.,  the  rapid 
increase  of  the  deflection  and  the  destruction  of  the  adhesion.  The  regulations 
require  the  help  afforded  by  the  concrete  to  be  neglected  in  calculating  the  tension 
in  reinforcements  as  the  reinforcements  have  to  resist  the  whole  tension 
across  any  crack  that  may  be  formed.  Diminution  of  adhesion  as  a  result 
of  high  tension  is  likely  to  take  place  only  at  the  centre  of  simple  spans  or  over 
the  supports  of  a  continuous  beam.  In  the  former  case  the  shear  near  the  middle 
of  the  span  is  generally  small,  but  at  the  supports  of  a  continuous  girder  the  shears 
are  maxima,  so  that  in  this  case  care  must  be  taken  that  the  slipping  stress  is  not 
excessive. 

The  maximum  compression  fixed  for  concrete  implies  a  certain  shortening 
of  the  latter,  and  consequently  of  the  steel  embedded  in  it.  The  compression  corre- 
sponding to  this  strain  of  the  steel  is  always  well  within  half  the  elastic  limit. 

The  Commission  proposed  as  a  factor  of  safety  for  the  concrete  of  3'5,  owing 
to  the  large  influence  workmanship  has  on  its  qualities. 

Simplification  of  the  Calculations. 

In  Table  No.  22,  on  p.  70,  in  the  figures  making  comparison  of  the  strength 

of  columns  reinforced  with  longitudinal  bars  intertied,  the  effects  of  the  longitudinals 

and  the  interties  are  not  separated,  and  the  coefficient  of  equivalence  is  taken  at  the 

same  value,  8  to  1 5  for  both.     This  is  to  some  extent  justified  by  an  examination 

R.C.  G 


82 


REINFORCED    CONCRETE. 


of  the  Stuttgart  results.  There  three  types  of  column  were  tested,  which  in 
addition  to  the  longitudinal  bars  of  0-591  inch  diameter,  had  interties  spaced  at 
9*84,  4'92  and  2*46  inches.  Differences  of  resistance  were  found  varying 
from  8*2  to  14 '6  tons  per  square  inch  of  the  section  of  the  equivalent 
longitudinal  bar,  having  a  volume  equal  to  that  of  the  ligatures.  These  figures 
correspond  to  the  figures  given  by  the  longitudinal  bars. 

On  the  contrary,  longitudinals  and  spirals  produce  widely  different  effects,  which 
must  not  be  confounded  in  calculations.  In  order  that  steel  of  middling  quality 
may  give  a  resistance  of  about  16  tons  per  square  inch,  which  is  generally  about  its 
apparent  limit  of  elasticity,  it  must  undergo  a  contraction  of  about  O'l  per  cent. 
Spiralled  concrete  supports  before  crushing  contractions  of  from  1  to  3  per  cent. 
The  resistances  provided  by  the  enclosed  longitudinal  bars  are  thus  not  less  than 
16  tons  per  inch2,  and  are  not  much  beyond  this  figure,  as  once  the  yield  point 
is  passed  the  resistance  increases  but  slowly  with  the  strain.  It  follows  that  one 
is  very  near  the  truth  in  deducting  from  the  total  resistance  of  a  spiralled  column, 
first  the  resistance  of  the  non-reinforced  prism  of  the  same  dimensions,  then  the 
resistance  of  the  longitudinal  bars,  reckoned  at  16  tons  per  square  inch,  and 
attributing  the  remainder  of  the  effect  to  the  spiralling. 

In  Table  No.  23  the  results  are  given  of  this  calculation  made  for  the  columns 
figuring  in  Table  No.  22  (division  8,  marked  (1)  to  (12)),  which  fulfilled  the  conditions 
indicated  by  the  Commission,  and  which  did  not  buckle.  The  second  horizontal 
row  gives  the  increase  in  strength,  after  deducting  the  resistance  of  the  non-rein- 
forced comparison  columns,  reckoned  in  tons  per  square  inch  of  the  equivalent  longi- 
tudinal reinforcing  bar,  having  the  same  volume  as  the  whole  of  the  metallic 
reinforcing.  The  lowest  line  gives  the  results  when  the  equivalent  longitudinal  bar 
has  the  same  volume  as  the  spirals  only,  and  when  in  addition  to  the  resistance  of  the 
non-reinforced  comparison  columns,  the  resistance  of  the  longitudinal  reinforcement 
is  also  deducted. 


TABLE  No.   23. 


1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

32-4 

26-0 

28-3 

36-2 

35-2 

28-6 

39-4 

35-6 

35-6 

33-0 

36-8 

40-0 

65-4 

36-0 

35-2 

45-4 

44-5 

32-4 

49-5 

43-8 

43-8 

49-5 

55-8 

57-8 

These  figures  complete  the  elements  necessary  for  the  design  of  compression 
pieces. 

The  Commission  pointed  out  that  there  is  necessarily  no  hard-and-fast  division 
between  longitudinally  reinforced  columns  and  spiralled  columns  ;  the  two  types 
merge  into  each  other  in  their  extreme  examples,  but  that  the  role  of  longitudinal 
reinforcement  is  essentially  different  from  that  of  transverse  reinforcement,  the 
former  actually  resisting  the  longitudinal  stress,  the  latter  simply  helping  the 
enclosed  concrete  to  resist  it. 

The  Commission  suggested  values  of  m  the  coefficient  of  equivalence  of  the  longi- 
tudinal reinforcement  and  the  concrete  varying  from  8  to  15.  Similar  values  for 
ra'  would  apply,  as  previously  explained,  to  the  lateral  interties  between  the 
longitudinals,  whilst  for  spiralling  the  values  of  m  would  vary  from  8  to  32.  In 


CALCULATION   OF   CRUSHING  RESISTANCE 


83 


every  case  stress  was  laid  on  the  necessity  for  keeping  the  compression  of  the  concrete 
within  62  per  cent,  of  the  resistance  of  non-reinforced  concrete. 

Although  in  the  later  stages  of  the  test  of  a  reinforced  column  the  spiralled 
core  alone  resists  the  whole  load,  it  is  not  advisable,  except  under  certain  circum- 
stances, to  complicate  the  calculations  by  relating  the  resistance  to  the  area  of  the 
core  instead  of  to  the  total  area  of  the  column.  It  might  be  advisable  to  do  so 
when  the  ratio  of  the  total  section  to  the  core  differed  from  140  or  150  to  100. 

So  long  as  the  ratio  of  length  of  a  column  to  its  least  transverse  dimension  is 
not  more  than  20,  no  calculations  relating  to  buckling  need  be  made. 

When  buckling  must  be  taken  into  account,  either  Euler's  or  Rankine's 
formula  may  be  used.  The  former  is  rigorously  applicable  only  to  perfectly 
straight  and  symmetrical  pieces,  and  for  its  application  the  modulus  of  elasticity 
for  all  the  stresses  concerned  must  be  known.  As  the  modulus  of  elasticity  of 
concrete  does  not  fall  below  950  tons  per  square  inch,  the  resistance  to  buckling 
of  non-reinforced  columns  may  be  calculated,  using  that  figure  (see  p.  17). 

For  reinforced  columns  of  the  ordinary  type  the  section  As  of  metal  may  be 
replaced  by  a  section  mAs  of  concrete  and  Euler's  formula  applied,  using  the  above- 
mentioned  value  for  the  modulus  of  elasticity,  m  having  the  values  previously 
defined. 

In  the  case  of  a  strongly  spiralled  column,  where  the  stress  that  might  be 
applied  without  fear  of  crushing  approaches  that  at  which  the  limit  of  elasticity 
rapidly  diminishes,  the  question  is  rather  more  complicated. 

In  Table  No.  22  there  is  indicated  the  resistance  attributed  to  the  reinforce- 
ment, but  in  studying  buckling  the  total  resistance  of  each  column  has  to  be  taken 
into  account.  This  is  given  in  division  4  -of  Table  No.  24. 

It  was  pointed  out  on  p.  74  that  the  resistance  of  the  comparison  columns 
varied  from  2,090  Ibs.  to  3,440  Ibs.  per  "square  inch.  In  order  to  render  the 
figures  comparable  amongst  themselves,  it  was  necessary  to  correct  the  observed 
resistances  to  those  which  would  have  been  obtained  if  the  concrete  had  had  a 
uniform  resistance  of  2,280  Ibs.  per  square  inch. 

In  division  7  of  Table  No.  24  there  is  indicated  the  resistances  to  crushing,  cal- 
culated by  attributing  to  the  concrete  a  resistance  of  2,280  Ibs.  per  square  inch, 
together  with  a  coefficient  of  equivalence  of  15  for  the  longitudinal  and  32  for  the 
spiral  reinforcements. 

TABLE  No.   24. 


1. 

2. 

3. 

4. 

5. 

6. 

7. 

Lengths 
of 
Columns. 

Percentage 
of  Longi- 
tudinal 
Bars. 

Percentage 
of 
Spirals. 

Maximum  Load 
Supported  in  Ibs. 
per  square  inch  of 
Total  Section. 

Corrected  Loads 
lor  Columns 
which  Crushed. 

Corrected  Loads 
for  Columns 
which  Buckled. 

Calculated 
Crushing 
Resistances. 

Feet. 

Lbs.  per 
square  inch. 

Lbs.  per 
square  inch. 

Lbs.  per 
square  inch. 

6-56 

1-42 

4-92 

7,280—6,690 

6,350 

6,110 

6,325 

6-56 

1-42 

3-49 

7,035—6,510 

— 

5,870—6,170 

5,290 

6-56 

1-42 

3-46 

6,110—5,840 

— 

4,950—5,930 

5,260 

7-54 

1-15 

2-58 

6,270—5,830 

5,570 

5,220 

4,550 

8-53 

0-91 

2-05 

5,460—4,805 

4,635 

4,510 

4,080 

9-84 

0-69 

1-64 

4,270—4,223 

4,135 

3,430 

3,690 

13-12 

0-91 

1-09 

4,350—3,780 

3,968 

— 

3,400 

13-12 

0-91 

1-13 

4,080—3,880 

3,550—4,070 

3,810 

3,370 

G    2 


84 


REINFORCED   CONCRETE 


In  each  case,  with  one  exception,  the  crushing  loads  are  in  excess  of  those 
calculated.  In  the  case  where  the  crushing  load  was  actually  less  than  the  cal- 
culated crushing  load,  the  percentage  of  reinforcement  was  the  greatest,  the 
longitudinals  amounting  to  1'42  per  cent,  and  the  spirals  to  4-92  per  cent.  The 
draft  regulations  suggested  by  the  Commission  indicated  that  the  ratio  between 
the  percentage  of  longitudinal  reinforcement  and  spiral  reinforcement  should  not 
fall  below  J.  In  the  column  in  question  this  condition  was  not  observed,  and, 
further,  the  pitch  of  the  spirals  (0'39  inch)  did  not  allow  of  good  ramming. 

It  may  be  observed  also,  taking  into  account  the  general  behaviour  of  the 
phenomena,  rather  than  the  anomalies,  that  the  loads  which  have  produced 
buckling,  corrected  as  above  described,  are  greater  than  the  calculated  resistances 
to  crushing. 

If,  thus,  for  a  column  having  the  same  proportions  and  the  same  percentage 
reinforcement  as  one  or  other  of  the  columns  tested,  the  crushing  resistance  is 
calculated  by  the  above  method,  using  any  given  factor  of  safety  from  that  point  of 
view,  then  as  regards  buckling  the  factor  of  safety  will  be  at  least  equal  to  that 
chosen  against  crushing. 

It  will  be  the  same  in  a  greater  degree  for  columns  less  reinforced  than  those 
the  results  of  which  are  tabulated,  since  the  modulus  and  the  limit  of  elasticity  on 
which  depend  the  resistance  to  buckling  diminish  much  less  quickly  with  the 
percentage  of  metal  than  the  resistance  to  crushing  actual  or  calculated. 

For  analogous  reasons  buckling  precedes  crushing  for  columns  more  strongly 
spiralled  than  those  experimented  on,  but  all  risk  is  avoided  if  the  load  applied  to 
a  column  is  not  allowed  to  exceed,  however  high  the  percentage  reinforcement,  the 
safe  load  for  the  column  of  the  same  proportions  in  the  series  of  experiments  in 
question. 

This  limitation,  although  not  quite  logical,  will  not  impose  any  undue  restraint 
on  constructors,  because  the  percentage  reinforcement  chosen  for  the  columns  of 
various  proportions  was  not  arrived  at  by  chance,  but  as  the  result  of  earlier 
experiment  to  determine  the  most  efficient  percentage  for  the  columns  of  varying 
proportions. 

The  most  efficient  percentage  for  the  shorter  columns  was  found  to  be 
about  3*5  per  cent.,  and  it  is  possible  that  for  the  slenderest  column  slightly 
greater  resistances  might  be  obtained  by  higher  percentage  reinforcement  than 
1'09  or  1-13. 

The  limits  of  load  deduced  from  the  experiments  are  given  in  Table  No.  25 
and  were  determined  as  follows  : — 

The  ratios  of  length  to  least  dimension  were  plotted  as  abscissae,  and  the  load 
supported  by  the  different  columns  as  ordinates.  The  mean  curve  was  traced  by 
suggestions  of  the  known  forms  of  the  curves  of  resistance  to  buckling.  The 
ordinates  of  this  curve  divided  by  4  gave  the  values  appearing  in  Table 
No.  25. 

TABLE  No.   25. 


length  • 

10 

11-5 

13 

15 

17 

20 

3  least  dimension 

Maximum  working  compression, 

1,422 

1,266 

1,138 

995 

924 

853 

Ibs.  per  square  inch. 

COMPRESSION  WITH   BENDING  85 

To  indicate  the  extent  of  the  anomalies  observed,  it  suffices  to  say  that  if 
instead  of  the  mean  values  obtained  by  the  curve,  the  actual  extreme  values  had 
been  taken  account  of,  the  factor  of  safety  given  by  the  above  figures  instead  of 
being  uniformly  4  would  have  varied  from  3*5  to  4*8. 

The  limits  of  pressure  just  indicated  are  suitable  for  concrete  having  a 
resistance  of  2,275  Ibs.  per  square  inch  when  tested  in  short  columns  between 
the  heads  of  an  hydraulic  press. 

Columns  in  buildings  are  under  conditions  at  least  as  favourable  when  the 
members  on  which  they  rest  as  well  as  those  they  support,  and  to  which  they  are 
strongly  bound  by  the  prolonged  reinforcements,  might  be  considered  as  exempt 
from  angular  displacements.  When  the  loading  in  such  cases  is  unsymmetrical, 
it  will  be  observed  that  it  is  less  than  the  maximum  in  view  of  which  the 
column  has  been  designed. 

To  obtain  data  for  designing  a  column  which  has  to  be  subject  to  a  bending 
moment,  the  amount  of  which  it  is  impossible  to  calculate,  such  as  that  due  to 
an  eccentricity  of  the  load,  the  Commission  experimented  on  eccentrically  loaded 
columns.  They  found  that  with  columns  reinforced  with  intertied  longitudinal 
bars,  when  the  load  was  applied  at  a  point  a  quarter  of  the  width  of  their  bases 
from  the  centre,  the  maximum  load  which  they  carried  was  equal  on  the  average  to 
60  per  cent,  of  the  maximum  load  of  columns  squarely  supported  between  the 
heads  of  the  press. 

A  spiralled  column  loaded  at  the  outer  edge  of  the  middle  third,  but  prevented 
from  acquiring  an  inclination  of  more  than  3 '4  in  100  at  the  ends,  conditions 
worse  than  any  to  be  met  with  in  practice,  the  resistance  was  not  sensibly  inferior 
to  that  of  a  similar  column  centrally  loaded. 

The  Commission  concluded  that  it  would  be  prudent  to  reduce  the  average  load 
on  columns  which  have  not  been  calculated  from  the  point  of  view  of  flexion  to 
60,  70  or  80  per  cent,  of  the  load  allowed  for  centrally  loaded  columns,  according 
as  the  column  is  placed  in  the  angles,  the  fa9ades  or  symmetrically  under  beams  in 
structures. 

Members  Subject  to  Compression  and  Bending. 

The  Commission  recommended  for  the  design  of  such  members  the  method 
which  attributes  to  each  element  of  the  material  a  stress  proportional  to  the 
product  of  its  longitudinal  deformation  and  its  corresponding  modulus  of 
elasticity. 

We  have  previously  seen  that  all  longitudinal  bars  of  metal  might  be  replaced 
by  cylinders  of  concrete  of  section  m  times  greater  than  that  of  the  metal,  and 
that  this  coefficient  of  equivalence  might  receive  the  same  value,  whether  it  was 
applied  to  resistance  or  elasticity.  These  experimental  results  are  equally 
applicable  to  bending  or  compression. 

Experiment  proves  that  concrete  is  capable  of  greater  shortenings  without  crush- 
ing in  bent  beams  than  in  columns,  so  that  the  reinforcements  in  the  former  develop 
more  fully  the  resistances  of  which  they  are  capable,  and  there  is  no  reason  to 
suppose  that  even  in  slabs  which  support  compression  in  conjunction  with  the 
bending  of  a  beam  are  the  values  of  the  resistances  less  than  in  columns  strongly 
reinforced.  The  maximum  value  of  m  should  thus  be  applied  to  members  under 
simple  bending. 

On  the  other  hand,  it  may  be  necessary  to  reduce  the  value  of  m  if 
precautions  are  not  taken  to  assure  maximum  efficiency  to  the  longitudinal  bars, 


86  REINFORCED    CONCRETE 

when  the  ratio  of  the  compression  produced  by  the  longitudinal  resultant  of  the 
exterior  forces  to  that  produced  by  the  bending  moment  rises. 

It  has  been  previously  explained  that  the  elastic  effect  of  transverse  reinforce- 
ments is  small,  and  even  although  the  resistance  of  a  properly  spiralled  member 
is  great,  yet  the  modulus  of  elasticity  at  high  stresses  is  low.  There  is 
consequently  no  reason  to  take  account  of  the  elastic  effect  of  the  transverse 
reinforcements  in  rcembers  subjected  to  bending,  whilst  the  elastic  effect  of  the 
longitudinals  is  fully  accounted  for  by  the  equivalent  increase  of  section  of  the 
concrete  from  the  point  of  view  of  resistance. 

To  simplify  the  calculations,  the  compressive  stress  in  members  subject  to 
bending  is  taken  as  proportional  to  the  deformation,  and  the  tensions  in  the 
concrete  are  not  taken  account  of.  It  is  evident  that  the  tensions  should  not  be 
taken  account  of,  because  at  the  crossing  of  the  minute  cracks  which  cannot  always 
be  avoided,  the  whole  load  is  taken  by  the  reinforcements.  In  other  respects  the 
tensions  of  the  concrete  are  not  negligible,  as  they  influence  not  only  the  deforma- 
tion of  the  neutral  line,  but  its  position  in  the  cross  section.  It  is  established  by 
experiment  that  within  the  limits  of  working  stress,  cracks  have  no  sensible 
influence  on  the  deformations  of  bent  members  or  on  the  crushing  of  compressed 
members.  From  this  point  of  view  the  concrete  ought  to  be  treated  as  if  it  produced 
everywhere  the  tension  of  which  it  was  capable. 

When  the  tensions  in  a  member  subject  to  bending  are  not  taken  account  of, 
the  total  calculated  compression  must  be  augmented  to  furnish  the  necessary 
moment  of  resistance,  so  that  the  calculated  value  of  the  maximum  compression  is 
increased  above  what  is  really  its  actual  value.  The  error  is  the  greater  the 
greater  the  proportion  the  tension  omitted  from  the  calculations  bears  to  the 
tension  value  of  the  reinforcement — i.e.,  the  error  is  the  greater  the  lower  the 
percentage  of  reinforcement. 

This  error  may  to  some  extent  be  compensated  for  in  the  choice  of  the  value 
of  the  ratio  m.  By  increasing  the  value  of  m  above  its  true  value — i.e.,  by 
exaggerating  the  superiority  of  the  elasticity  of  metal  over  that  of  concrete,  the 
extensions  calculated  for  the  former  are  reduced  and  the  shortenings  calculated  for 
the  latter  are  increased.  A  greater  cross-sectional  area  of  concrete  is  thus  required 
over  which  the  compression  component  of  the  resisting  moment  is  distributed.  The 
result  of  using  such  an  inflated  value  of  m  is  virtually  to  lower  in  the  beam  the 
calculated  position  of  the  neutral  axis,  and  to  reduce  the  calculated  value  of  the 
maximum  compressive  stress.  The  absolute  values  of  the  two  kinds  of  contrary 
errors  thus  committed  vary,  if  not  proportionally,  at  least  in  the  same  sense  :  both 
are  maxima  in  slabs  and  beams  of  rectangular  sections  and  minima  in  beams  of  T 
section  formed  of  a  slab  and  rib. 

The  error  committed  in  neglecting  the  tensions  of  the  concrete  is  less  as  the 
percentage  of  the  reinforcement  is  increased,  whilst  the  error  resulting  from  the 
exaggeration  of  m  is  less  as  the  ratio  of  thickness  of  slab  to  height  of  rib  is 
reduced.  These  errors  compensate  in  a  sufficiently  satisfactory  manner  in  slabs 
and  beams  of  whatever  proportions. 

In  fixing  on  15  as  the  value  of  m,  the  ratio  between  the  modulus  of  elasticity 
of  steel  to  that  of  concrete  in  compression,  the  following  considerations  influenced 
the  Commission  : — 

The  modulus  of  elasticity  of  concrete  in  compression  varies  from  1,020  tons  per 
square  inch  to  2,540  tons  per  square  inch  under  light  loads,  the  former  applying 
to  concrete  gauged  with  excess  of  water  and  imperfectly  rammed,  the  latter 
containing  only  the  water  necessary  for  its  use  and  thoroughly  rammed. 


ADHESION  87 

A  high  modulus  of  elasticity  is  generally  accompanied  by  a  high  resistance,  and 
vice  versa. 

It  must  be  remembered  that  as  the  stress  increases,  the  value  of  the  modulus 
of  elasticity  is  reduced,  and,  consequently,  the  lowest  value  which  can  be  met 
with  under  working  circumstances  must  be  used.  This  has  been  taken  as  933  tons 
per  square  inch,  and  as  the  modulus  of  elasticity  of  the  steel  generally  used  is  about 
14,000  tons  per  square  inch,  the  value  of  m  is  15.  The  value  of  the  compressive 
stress  to  be  allowed  in  the  concrete  is  closely  related  to  the  value  of  m.  The 
higher  the  value  of  m  chosen,  the  lower  the  compressive  stress  which  ought  to  be 
reckoned  on. 

Adhesion  of  the  Concrete  to  the  Metal. 

Assuming,  according  to  the  elementary  theory  of  perfectly  elastic  bodies,  that 
the  tendency  to  slip  at  any  section  is  proportional  to  the  shearing  stress  on  that 
section,  the  resistance  offered  to  the  slipping  of  the  longitudinal  reinforcements 
has  been  calculated,  in  the  beams  of  the  first  series  which  failed  in  that  way,  at 
from  170  to  213  Ibs.  per  square  inch  of  the  area  of  contact.  In  many  existing 
works  the  same  mode  of  calculation  indicates  values  as  high  as  142  Ibs.  per  square 
inch  as  the  measure  of  the  tendency  to  slip. 

The  Commission  carefully  considered  the  question  whether  common  practice  in 
this  respect  ought  to  be  modified,  keeping  in  view  the  difficulty  of  doing  so  without 
largely  increasing  the  cost  or  hindering  the  ramming. 

Experiment  showed  that  in  the  relative  slipping  of  the  reinforcement  and  the 
concrete,  as  in  the  other  deformations  of  reinforced  concrete,  a  gradual  diminution 
in  the  modulus  of  elasticity  took  place  as  the  stress  was  augmented,  and  after  the 
real  elastic  adhesion  was  destroyed,  the  frictional  resistance  to  slipping  was  still 
considerable. 

In  the  second  series  of  bending  tests  it  was  found  that  with  beams  similar 
in  all  respects  to  those  of  the  first  series,  but  supported  about  1  foot  4  inches 
from  one  end  instead  of  about  4  inches  as  in  the  first  series,  failure  did  not  take 
place  by  slipping  of  the  reinforcements.  This  fact  is  explained  by  the  additional 
resistance  to  slipping  which  the  reinforcements  obtained  from  the  part  beyond  the 
supports.  According  to  theory,  however,  the  shearing  stress  was  zero  there, 
and  in  consequence  there  should  have  been  no  additional  resistance  to  slipping 
obtainable  from  this  part. 

To  investigate  this  point,  the  longitudinal  slipping  was  measured  in  two  places, 
one  between  the  support  and  the  load  when  the  shear  and  presumably  the 
tendency  to  slip  was  maximum  and  constant,  the  other  in  the  projection  beyond  the 
support  when  the  shear  was  everywhere  zero.  It  was  found  that,  up  to  a  certain 
limit,  the  observed  facts  agreed  with  the  theory.  The  slipping  was  zero  outside 
the  supports,  but  between  the  load  and  the  support  it  had  quite  an  appreciable 
value,  which  varied  with  the  load.  Beyond  a  certain  value,  slipping  occurred 
throughout. 

These  facts  led  to  the  following  conclusions : — 

So  long  as  the  elasticity  as  regards  slipping  is  intact,  the  hypothesis  that  the 
slipping  forces  are  proportional  to  the  shearing  forces  is  nearly  correct.  When,  how- 
ever, the  elasticity  has  been  reduced  or  broken  down  at  a  part,  the  slipping  spreads 
itself  over  the  whole  length  of  the  reinforcement,  and  equilibrium  is  established  with 
the  maxima  stresses  sensibly  inferior  to  those  indicated  by  the  formula.  This  would 
explain  the  phenomena  observed  in  the  experiments,  and  this  interpretation  may  be 
exhibited  graphically  by  Fig.  27  for  the  case  of  a  beam  with  a  concentrated  load  or 


88 


REINFORCED   CONCRETE 


with  a  distributed  load.  The  ordinates  of  the  full  straight  line  represent  the  shear 
at  the  various  sections  in  the  half  span,  those  of  the  dotted  curved  line  the  slipping 
stress  at  these  sections,  and  in  the  part  of  the  beam  overhanging  the  support. 

These  considerations  have  led  the  Commission  to  the  view  that  a  low  unital 
stress  should  be  adopted  for  slipping  where  no  additional  resistance  can  be  given ; 
but  where  additional  resistance  to  slipping  is  obtainable,  while  its  exact  calculation 


Diagram    For    Concentrated    Load. 


K 


Diagram    for    Distributed    Load . 
FIG.  27. 

may   not  be  possible,    some  allowance  should   be  made  by  increasing   the  stress 
allowed. 

Transverse  Reinforcement  of  Members  subject  to  Bending. 

In  ribbed  beams  transverse  reinforcements,  either  alone  or  with  the  help  of 
longitudinal  tension  reinforcement  raised  up  towards  the  ends  calculated  to  resist 
the  shear,  are  generally  used,  whilst  in  slabs  where  the  ratio  of  the  depth  to  span 
is  not  excessive  no  transverse  reinforcements  are  generally  employed. 

The  Commission  thinks  the  practice  justified  for  the  following  reasons : — 
The  ribs  are  generally  executed  several  days  before  the  slabs,  and  unless  great 
care  is  exercised,  and  even  then,  the  junction  between  the  two  portions  forms  a  decided 
plane  of  weakness,  and  slipping  can  only  be  prevented  by  reinforcements  passing 
across  this  plane.  These  reinforcements  should  be  capable  of  resisting  the  whole 
of  the  tendency  to  slip  on  that  plane,  and  consequently  they  must  be  able  to  resist 
the  shearing  force. 


TRANSVERSE   REINFORCEMENT  89 

On  the  other  hand,  slabs  are  usually  put  in  in  one  operation,  and  it  is  thus  only 
from  the  point  of  view  of  rupture  across  the  full  concrete  that  their  resistance  to 
shear  ought  to  be  assured. 

So  long  as  it  is  not  fissured  concrete  resists  shearing,  and  when  the  reinforcement 
is  less  than  1  per  cent.,  a  stress  of  65  Ibs.  per  square  inch  may  be  resisted.  The 
resistance  of  intact  slabs  is  thus  generally  assured  by  the  concrete  alone.  The 
experimental  slabs  loaded  to  destruction  perished  not  by  oblique  shearing,  but  by 
elongation  of  the  reinforcements  and  crushing  of  the  concrete.  The  beam  P,  on  p.  36, 
without  transverse  reinforcements  continued  to  resist  shear  after  the  formation  of 
oblique  fissures  cutting  across  more  than  five-sixths  of  the  section.  The  shearing  force 
could  only  have  been  equilibrated  in  the  planes  of  the  cracks  by  the  transverse 
resistance  of  the  longitudinal  reinforcements,  and  by  a  kind  of  friction  developed  in 
the  particles  of  the  compressed  concrete  remaining  in  contact  in  the  prolongation  of 
the  fissures. 

In  this  connection  it  may  be  pointed  out  that  the  resistance  longitudinal  reinforce- 
ments present  to  shearing,  vertical  or  oblique,  is  always  superior  to  the  shearing 
effort,  aiid  that  except  in  beams  carrying  all  the  load  concentrated  in  a  single  point, 
the  tension  of  the  reinforcements  diminishes  as  the  shearing  effort  increases  to  such 
an  extent  that  there  remains  sufficient  free  resistance  in  the  metal  to  resist  the 
shear. 

The  longitudinal  reinforcements  are  thus  almost  always  sufficient  to  prevent 
rupture  on  oblique  planes  in  beams  of  whatever  dimensions  if  the  solidity  of  the 
enveloping  concrete  is  assured.  The  danger  of  the  concrete  itself  breaking  up  is 
less  when  the  percentage  reinforcement  is  low,  and  when  it  is  split  into  as  many 
bars  as  possible. 

Slabs  are  thus  well  conditioned  from  both  these  points  of  view,  and  it  is  not 
generally  necessary  to  employ  transverse  reinforcements,  the  number  and  weakness 
of  temporary  fixing  of  which,  render  ramming  difficult.  If,  however,  the  ratio  of 
depth  to  span  is  great,  and  consequently  the  longitudinal  reinforcements  small  in 
respect  to  the  shearing  effort,  there  should  be  added  transverse  reinforcements 
calculated  to  resist  the  shearing  effort  with  the  help  of  the  concrete  and  the 
longitudinal  reinforcements. 

Empirical    Formulae. 

The  Commission  recognised  the  necessity,  in  structures  where  the  calculation 
of  the  dimensions  from  a  purely  theoretical  basis  would  be  too  complicated  for 
practical  purposes,  of  the  use  of  empirical  expressions.  The  following  observations 
were  made  regarding  the  basis  on  which  such  expressions  should  rest  so  as  not  to 
be  irrational  or  to  conflict  with  known  facts. 

In  a  structure  of  ribs  and  slabs,  the  ribs  impose  almost  completely  their 
longitudinal  deformations  on  the  contiguous  portions  of  the  slabs  they  support, 
the  effect  dying  out  with  distance  from  the  rib. 

It  is  covnenient,  as  previously  described,  to  allow  that  for  a  fixed  width  on 
both  sides  of  each  rib  the  slab  is  completely  solid  with  it  from  the  point  of 
view  of  bending,  the  solidarity  ceasing  abruptly  outside  this  width. 

In  the  case  of  highly  concentrated  loads,  such  as  a  wheel  load,  the  pressure 
is  transmitted  not  only  vertically  but  obliquely,  forming  a  kind  of  cone,  the 
base  of  which  has  greater  dimensions  the  greater  the  total  thickness  of  causeway, 
filling  and  slab.  The  unloaded  parts  outside  this  imaginary  conical  zone  participate 
in  the  support  of  the  latter,  and  the  deformation  extends  transversely  the  greater 
the  span  of  the  slab.  Any  expression  for  the  distribution  of  such  a  load  ought 


90  REINFORCED   CONCRETE 

thus  to  contain  as  variables  the  combined  thicknesses  of  causeway,  filling  and  slab 
and  the  span  of  the  latter.  The  coefficients  should  be  determined  by  the  analysis 
of  experimental  results,  and  so  as  to  give  results  conform  to  successful  practice. 

In  the  case  of  slabs  carried  by  two  sets  of  beams  at  right  angles,  the 
problem,  analogous  to  that  of  a  plate  supported  or  fixed  along  all  four  sides,  is 
complicated  by  the  heterogeneity  of  the  material.  Any  expression  used  should  give 
the  results  as  for  ordinary  beams  when  the  spans  are  infinitely  different,  and  when 
they  are  equal  should  give  results  agreeing  with  successful  practice. 

In  considering  the  division  of  the  loads  between  parallel  beams,  it  is  not  possible 
to  do  more  than  keep  in  view  the  principle  of  the  solidarity  of  the  main  beams,  the 
secondary  beams  and  the  slabs,  which  can  only  be  applied  by  reference  to  experi- 
ments on  analogous  works. 

Tests. 

The  importance  of  rapid  tests  by  rolling  load  has  been  drawn  attention  to  in 
the  regulations,  as  the  deformations  resulting  from  variations  of  temperature  during 
tests  of  longer  duration  are  frequently  of  the  same  order  as  those  produced  by  dead 
loads. 


CHAPTER  VII 
OF  NOTES  PRESENTED  BY  M.  CONSIDERS 

A.  Tension  Tests  on  Prisms  of  Reinforced  Concrete.  - 

THE  description  and  particulars  of  the  tests  are  given  in  Chapter  IV.,  5,  p.  23, 
and  the  results  are  exhibited  graphically  in  Fig.  28,  p.  92. 

Precautions  were  taken  to  prevent  any  twisting  of  the  test  pieces,  and  the 
measurements  taken  showed  that  they  were  successful,  consequently  the  variations 
produced  by  the  loading  and  unloading  give  reliable  information. 

In  the  test  pieces  the  area  of  the  concrete  was  15*5  square  inches  and  the  area 
of  the  metal  0*175  square  inch,  and  its  modulus  of  elasticity  29 '1  x  106  Ibs.  per 
square  inch. 

An  elongation  d  I  in  the  prism,  which  produces  the  total  augmentation  of  tension 
d  T,  produces  in  the  reinforcement  an  algebraical  augmentation  of  tension  dtm,  equal 
to  d  I  X  0-175  X  29-1  X  106  Ibs.,  and  the  difference  d  T  —  dtm  is  the  increase  in 
the  tension  in  the  concrete  which  the  elongation  has  produced.  To  deduce  from 
the  variations  of  tension  thus  determined  the  absolute  tensions  of  the  concrete 
or  the  steel,  it  is  necessary  to  know  the  reciprocal  and  equal  reactions  between 
the  associated  materials  at  the  beginning  or  the  end  of  the  period  during  which  the 
variations  have  been  studied. 

The  twenty-fifth  and  last  unloading  of  an  experimental  prism  (No.  3  prism),  during 
which  the  total  tension  was  reduced  from  3,945  Ibs.  to  441  Ibs.,  the  minimum 
load  necessary  to  keep  the  whole  apparatus  taut,  may  be  taken  as  an  example. 

The  point  where  the  pencil  stopped  is  indicated  on  Fig.  28  by  the  letter  .4,  and 
if  the  irregularities  due  to  the  apparatus  are  overlooked,  it  is  seen  that  the  curve 
of  unloading  differs  little  from  a  straight  line,  so  that  without  appreciable  error  it  may 
be  taken  that  if  the  unloading  had  been  finished,  the  curve  of  unloading  would 
have  been  a  straight  line  terminating  at  B. 

To  determine  the  reciprocal  reactions  between  the  concrete  and  the  reinforce- 
ment, the  length  of  one  of  the  reinforcements,  the  ends  of  which  projected  beyond 
the  ends  of  the  prism,  was  measured.  The  concrete  overlying  this  reinforce- 
ment was  then  very  carefully  removed,  and  the  reinforcement  slackened  in  its  bed, 
but  without  destroying  the  latter,  so  as  to  conserve  the  curves  which  would  influence 
its  length.  The  increase  in  length  was  found  to  be  '00433  inch  on  a  length  of 
55-12  inches.  The  contraction  which  the  adhesion  between  the  concrete  and  the 
reinforcement  had  imposed  on  the  latter  even  after  twenty-five  applications  of  a 
load  of  3,945  Ibs.  was  thus  0-008  per  cent. 

To  completely  annul  the  compression  which  the  contraction  of  the  concrete 
had  imposed  on  the  reinforcement,  it  would  have  been  necessary  to  have  increased 
the  length  of  the  prism  by  0*008  per  cent. ;  that  is,  to  take  it  to  the  point  marked 
C  on  the  diagram.  If  through  this  point  of  equilibrium  of  the  reinforce- 
ments a  straight  line  FF'  is  drawn  having  an  inclination  to  the  horizontal  of 
0-175  X  29-1  X  106  to  1,  then  each  vertical  intercept  between  FF'  and  00' 
represents  algebraically  the  tension  in  the  reinforcement  at  that  phase. 


92 


REINFORCED   CONCRETE 


The  tension  produced  by  the  concrete  at  any  deformation  is  measured  by  the 
intercept  between  the  deformation  curve  and  the  line  FF'. 


9000 


7000 


5000 


3000 


1000 


/oool, 

2000 


5000 
3000 

1000 
0 

1000^ 
2000 


Prism     N°   I 


0-05 


0-10 


O-I5 


Prism    N9   2 


-^==- 

^  —  F 

^ 

^.  —  - 

/ 

> 

r    ./ 

^* 

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.    Elongation  per  Cent,  of 

FIG.  28. 


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Since  the  prisms  were  made  of  the  same  materials  with  equal  care  and  by  the 
same  workmen,  it  might  be  allowed  without  sensible  error  that  the  line  FF'  has 
the  same  relation  to  the  origin  of  the  four  deformation  curves. 


ANALYSIS   OF   TENSION   TESTS  93 

The  following  inferences  can  be  drawn  from  the  four  graphs  : — 

1°.  Initial  State. 

To  obtain  the  true  origin  the  deformation  curve  must  be  continued  back  to  the 
zero  load-line  at  the  inclination  it  has  immediately  above  the  440  Ibs.  load-line. 
The  intercept  OD  measures  the  tension  in  the  concrete  due  to  its  being  prevented 
by  the  adhesion  of  the  reinforcements  from  taking  its  full  contraction.  This 
tension  amounts  to  1,146  Ibs.,  or  about  74  Ibs.  per  square  inch.  The  compression 
in  the  reinforcements  due  to  the  same  cause  is  1,146  Ibs.,  or  6,540  Ibs.  per  square 

inch.     This  compression  in  the  metal  corresponds  to  a  strain  of          ' — -g  ;  i.e., 

jy*  1X10 

of  2-25  X  10~4,  or  0-000225,  or  a  shortening  of  0-0225  per  cent. 

2°.  Elongation  ivithout  Cracking  oj  the  Concrete. 

Prism  No.  1  underwent  an  elongation  of  0-135  per  cent,  before  the  first  crack 
was  apparent  to  the  eye.  Prism  No.  2  underwent  a  maximum  elongation  of 
0'061  per  cent.,  with  repetitions  of  smaller  elongations,  without  apparent  injury. 
The  reinforcements  were  removed,  and  it  was  not  till  almost  the  end  of  the  operation 
of  cutting  out  that  a  crack  was  observed  which  cut  the  prism  into  two  parts  29  and 
10  inches  long  respectively.  The  operators  thought  that  this  crack  was  the  result 
of  the  cutting  out  of  the  reinforcement. 

Non-reinforced  concrete  of  the  same  quality  as  the  above  prism  does  not  appear 
to  undergo  without  breaking  an  elongation  of  more  than  0*008  per  cent.,  or  about 
one-eighth  of  the  elongation  undergone  by  prism  No.  2  without  breaking.  The  two 
portions  of  this  prism  were  subjected  to  bending,  and  gave  tension  resistances 
calculated  by  the  usual  formulae  of  125  and  133  Ibs.  per  square  inch,  figures  which 
are  not  far  removed  from  the  initial  tension  resistance  of  the  concrete  employed, 
and  which  had  not  been  previously  stressed. 

Reinforced  concrete  should  thus  take  without  breaking,  and  at  the  same  time 
conserving  a  large  part  of  its  resistance,  elongations  much  superior  to  those 
demanded  of  it  in  structures ;  but  it  is  also  evident  that  cracks  might  in  certain 
places  be  present  beforehand  or  develop  during  loading  of  which  it  will  be 
necessary  to  take  account  in  the  calculations  of  resistance. 

3°.  Law  of  Deformation  oj   Reinforced  Concrete. 

Measuring  from  the  different  graphs  the  tension  produced  by  the  concrete,  which 
is  indicated  by  the  intercept  between  the  graph  and  the  line  FF't  we  find  that  for 
elongations  of  0'004  per  cent.,  0-02  per  cent.,  0'06  per  cent,  to  0-135  per  cent.,  the 
tensions  in  the  concrete  were  170,  213  to  242  and  200  to  185  Ibs.  per  square  inch. 

During  the  elastic  period,  corresponding  to  an  elongation  of  less  than  0'004  per 
cent.,  the  tension  had  values  growing  regularly  till  a  limit  of  170  Ibs.  per  square 
inch  had  been  reached,  which  would  be  the  limit  of  the  resistance  to  tension  if  there 
were  no  reinforcement. 

As  the  elongation  increases  from  0*004  per  cent,  to  0'02  per  cent,  the  tension 
increases  till  it  exceeds  from  30  to  40  per  cent,  the  resistance  to  tension  of  non- 
reinforced  concrete.  This  increase  disappears  on  further  increasing  the  elongation 
to  0'06  per  cent,  approximately,  and  afterwards  the  tension  remains  constant  and  at 


94  REINFORCED   CONCRETE 

the  value  of  the  resistance  of  non-reinforced  concrete  until  a  much  greater  elongation, 
about  0'135  per  cent.,  was  realised. 

If  for  simplicity  the  temporary  increase  of  resistance  above  referred  to  is 
neglected,  it  might  be  said  that  the  modulus  of  elasticity  of  reinforced  concrete  is 
the  same  as  that  of  non-reinforced  concrete,  so  long  as  the  applied  stress  does  not 
exceed  the  resistance  to  tension  of  the  latter.  When  that  tension  is  exceeded  the 
modulus  of  elasticity  is  reduced  to  zero,  and  in  the  places  where  there  are  no 
cracks  the  help  it  gives  to  the  reinforcements  is  not  zero  but  constant.  The 
variations  of  tension  in  the  reinforcements  during  this  period  are  equal  to  the 
total  variations  of  tension  in  the  prism,  since  the  resistance  of  the  concrete 
remains  sensibly  constant.  They  are  equal  to  the  product  of  the  variations  of 
their  lengths  by  the  coefficient  of  elasticity  of  the  metal,  and  might  thus  be 
calculated  whether  there  are  cracks  in  the  concrete  or  not. 

4°.  Loading  and  Unloading. 

As  will  be  observed  from  Fig.  28,  the  unloading  curve  is  very  different  from 
the  curve  of  first  loading.  It  is  almost  rectilinear,  and  presents  inclinations 
slightly  greater  at  the  ends  than  elsewhere. 

The  curve  of  reloading  differs  little  from  that  of  unloading ;  the  slight  curva- 
tures at  the  ends  are  in  opposite  directions.  The  mean  modulus  of  elasticity  is  the 
inclination  of  a  straight  line  through  the  extreme  ends  of  these  lines,  and  the 
greater  the  previous  elongation  the  lower  the  value  of  the  mean  modulus. 

5°.  Effects  of  Tension  on  the  Resistance  and  Elasticity  of  Concrete  to  Compression. 

In  some  structures,  e.g.,  arches,  the  concrete  might  be  submitted  alternatively 
to  tensions  and  to  compressions,  and  it  is  important  to  know  the  influence  that 
elongations  exceeding  the  elastic  limit  exercise  on  the  properties  of  the  concrete 
from  the  point  of  view  of  compression. 

A  portion  of  prism  No.  1,  which  had  undergone  the  considerable  elongation 
of  0*0135  per  cent.,  was  submitted  to  compression.  It  was  found  that  its  resistance 
to  compression,  which  before  the  tension  stress  was  applied  was  between  1,800  and 
2,000  Ibs.  per  square  inch,  had  fallen  to  between  1,570  and  1,650  Ibs.  per  square 
inch.  The  modulus  of  elasticity  was  reduced  from'  1,900  tons  per  square  inch 
to  950  tons  per  square  inch. 

These  results  are  reassuring,  because  the  diminutions  of  resistance  and  elasticity 
in  question,  of  which  the  former  is  small  and  the  second  presents  no  danger,  except 
from  the  point  of  view  of  buckling,  were  produced  by  an  elongation  five  to  eight 
times  greater  than  that  experienced  in  structures. 

6°.  Effect  of  Repetition  of  Loading. 

Prism  No.  3  was  submitted  to  the  application,  repeated  twenty-five  times,  of  a 
tension  of  3,950  Ibs.,  and  it  was  observed  that  towards  the  end  of  the  experiments 
the  deformations  no- longer  sensibly  increased.  By  the  method  already  described  of 
measuring  the  ordinates  from  the  graph  to  the  line  FF\  it  is  observed  that  the 
tension  in  the  concrete  is  reduced  from  235  to  185  Ibs.  per  square  inch — i.e.,  to 
80  per  cent,  of  its  initial  value. 

The  tests  made  at  Quimper  showed  that  the  final  value  was  reduced  to  0*70  of 
the  initial  value  after  many  thousand  repetitions. 


ANALYSTS   OF   TENSION   TESTS  95 


7°.  Final  State  after  Unloading. 

This  state  ought  to  be  considered  from  two  points  of  view,  of  which  the  first 
throws  light  on  the  second  : — 

1°.  The  reciprocal  reactions  of  the  concrete  and  the  metal. 

2°.  The  final  deformations  of  the  metal. 

In  order  to  determine  by  means  of  the  graph  of  prism  No.  3  the  state  of  interior 
equilibrium  which  compete  unloading  would  produce,  the  curve  of  unloading  HA 
must  be  continued  to  B.  The  intercept  between  B  and  FF'  gives  the  tension  in 
the  concrete,  which  divided  by  the  area  of  the  reinforcements  gives  the  unital 
compression  in  the  latter. 

It  is  evident  that  even  after  elongations  of  0'03  to  0'04  per  cent,  the  reinforce- 
ments still  retained  a  small  amount  of  the  initial  compression  imposed  on  them  by 
the  concrete. 

In  prism  No.  2,  after  an  elongation  of  0'061  per  cent.,  the  original  interior 
stresses  were  annulled,  and  stresses  of  a  contrary  sense  and  of  small  amount  were 
produced. 

In  prism  No.  1  the  interior  state  of  equilibrium  was  determined  by  measuring 
one  of  the  reinforcements  which  projected  beyond  the  ends  of  the  prism,  then 
releasing  it  from  the  concrete  and  measuring  it  again.  The  shortening  observed 
was  0-01  per  cent.  It  follows  that  after  this  prism  had  undergone  the  considerable 
elongation  of  0*135  per  cent.,  the  original  compression  in  the  reinforcements  was 
replaced  by  a  tension  of  O'Ol  X  100  X  29'1  X  106 — i.e.,  2,910  Ibs.  per  square 
jnch — which  equilibrated  a  compression  of  33  Ibs.  per  square  inch  in  the  concrete. 

The  inference  from  these  results  is  that  the  interior  reactions  produced  by  the 
contraction  of  the  concrete  are  reduced  by  the  effect  of  the  deformations,  and  may 
even  be  replaced  by  reactions  of  a  contrary  sense  when  the  elongations  exceeded  a 
limit  of  from  0'05  per  cent,  and  0*06  per  cent.,  which  is  greater  than  the  elongations 
met  with  in  actual  structures. 

This  fact  agrees  with  the  alteration  of  the  elasticity  of  concrete  by  large 
elongations.  It  is,  of  course,  in  virtue  of  its  elasticity  that  concrete  reacts  against 
the  reinforcements  either  in  tension  or  compression,  and  it  follows  when  this 
elasticity  is  reduced  the  property  previously  possessed  by  the  concrete  of  imposing 
stresses  on  the  reinforcements  is  diminished  or  lost. 

It  is  evident  that,  since  the  effects  of  large  but  not  excessive  tensions  is  to 
allow  the  reinforcements  to  return  to  their  normal  length,  the  contraction  of  con- 
crete kept  in  air  imposes  strains  of  the  same  order  on  the  reinforcements  as  the 
external  tensions. 

Where  the  concrete  has  been  immersed  in  water,  the  deformations  due  to  the 
contraction  of  the  concrete  are  much  less  than  when  the  concrete  is  kept  in  air. 

The  Quimper  experiments  confirm  the  above  facts.  It  may  be  mentioned  that 
the  average  reinforced  concrete  used  in  construction  is  not  submitted  to  elongations 
greater  than  from  0'015  to  0'030  per  cent. 

B.  Bending  Experiments  in  large  Reinforced  Concrete  Beams. 

All  the  beams  considered  here  are  13' 12  feet  long,  15*75  inches  deep  and  7-87 
inches  wide.  The  resume  of  the  methods  and  results  of  the  experiments  are  given 
in  Chapter  VI.,  section  9,  on  pp.  30 — 41,  and  only  the  main  features  of  the  results 
and  the  deductions  from  them  are  considered  here. 


96  REINFORCED   CONCRETE 

1°.  Initial  State. 

The  contraction  of  the  reinforcing  bars,  0*874  inch  diameter,  was  observed 
during  the  setting  of  the  concrete  by  measuring  the  over-all  length  of  one  of  the 
reinforcements  from  time  to  time.  The  reinforcement  showed  a  progressive 
shortening  averaging  0*0264  per  cent,  on  the  length  of  the  bar,  and  since  the 
contraction  at  the  ends  was  necessarily  zero,  the  maximum  shortening  which  would 
occur  at  the  middle  would  not  be  less  than  0*031  per  cent.  Further  contraction 
took  place  after  these  results  were  recorded,  so  that  it  is  probable  that  the  shorten- 
ing of  the  reinforcement  exceeded  considerably  0 '031  per  cent,  at  the  middle  of 
the  span  when  the  tests  were  made. 

As  a  check  this  figure  was  also  arrived  at  by  an  entirely  different  method. 
The  permanent  elongation  sustained,  by  the  reinforcement  during  the  test  was 
measured,  and  was  found  to  be  0*015  per  cent,  at  the  centre  of  the  span.  The 
reinforcement  was  freed  from  the  concrete  and  a  further  elongation  of  0*033  per 
cent,  was  recorded,  making  a  total  of  0*048  per  cent,  in  the  middle  part  of  the  beam. 
Thus,  making  allowance  for  unavoidable  inaccuracies,  it  is  concluded  that  for 
concrete  of  these  proportions  the  contraction  due  to  setting  in  the  middle  part  of  a 
beam  reinforced  as  described  would  be  from  0*035  per  cent,  to  0*040  per  cent. ;  and 
if  the  metal  had  a  modulus  of  elasticity  of  31*3  X  106  Ibs.  per  square  inch,  a 
compressive  stress  of  about  11,000  Ibs.,  or  about  5  tons  per  square  inch,  would  be 
produced. 

This  figure  is  much  greater  than  that  found  for  the  stress  in  the  tension  test 
pieces.  The  difference  is  partly  due  to  the  greater  dimensions  of  the  beam  and 
partly  to  the  better  quality  of  the  concrete.  It  is  evident,  of  course,  that  the 
tension  a  concrete  might  exercise  in  setting  would  be  proportional  to  its  resist- 
ance. 

2°.  Deformation  of  Plane  Sections. 

Four  beams  Avere  studied  from  this  point  of  view,  two  without  visible  fissures 
and  two  having  the  tension  part  of  the  beam  cut  through  by  the  interposition  of 
a  double  sheet  of  tin  foil. 

In  all  the  beams,  slit  or  otherwise,  the  indications  of  the  apparatuses 
measuring  the  deformations  of  the  concrete  gave,  when  plotted  on  a  diagram, 
almost  rigorously  straight  lines,  conformably  to  the  hypothesis  of  the  conserva- 
tion of  plane  sections  during  bending. 

In  the  beams  not  slit,  the  elongations  of  the  reinforcements  agreed  also  almost 
rigorously  with  the  same  hypothesis  ;  that  is  to  say,  were  sensibly  equal  to  those  of 
the  layers  of  concrete  at  the  same  distance  from  the  neutral  axis  of  the  beam  as 
the  reinforcement. 

It  was  otherwise,  however,  for  the  slit  beam,  where  it  was  found  that  slipping  of 
the  reinforcements  was  taking  place  towards  the  middle  of  the  span,  and  gradually 
increasing  with  increasing  bending  moment.  In  the  part  of  the  beam  under 
observation,  owing  to  the  method  of  applying  the  loads,  there  were  no  shearing 
stresses. 

The  observations  made  showed  very  considerable  warping  in  different  parts 
of  the  beam. 

3°.   Position  of  the  Neutral  Axis. 

It  is  important  to  compare  the  observed  positions  of  the  neutral  axis  with  those 
given  by  the  formulae  based  on  the  hypothesis  of  the  conservation  of  plane  sections, 


ANALYSIS    OF    BENDING   EXPERIMENTS 


97 


and  on  the  application  to  flexion  of  the  laws  of  deformation  of  reinforced 
concrete. 

From  the  tension  tests  previously  dealt  with  it  is  observed  that  the  deformation 
of  concrete  in  tension  presents  two  phases  separated  by  a  short  transition  period. 

In  the  first,  which  corresponds  to  very  small  elongations,  the  concrete  behaves 
as  a  perfectly  elastic  body.  In  beams  reinforced  only  on  the  tension  side,  such  as 
those  under  consideration,  the  neutral  axis  ought  to  be  situated  a  little  above  the 
middle  of  the  height,  in  virtue  of  the  superiority  of  the  elasticity  of  the  metal  over 
that  of  the  concrete  which  it  replaces. 

In  the  second  phase,  the  tension  of  the  stretched  concrete  remains  constant. 
The  position  of  the  neutral  axis  corresponding  to  the  additional  deformations 
produced  during  this  phase  ought  thus  to  be  the  same  as  if  the  tension  of  the 
concrete  was  zero. 

It  is  given  by  the  formula  :  1 


when 


x  =  n  _ 

distance  from  centre  of  tension  reinforcement  to  neutral  axis 

x  is  -  ;  - 


A,  the  distance  from  centre  of  reinforcements  to  the  upper  surface  of  the 

beam ; 
mw' 

n'   bh> 

6,  the  width  of  the  beam  ; 
w\  the  section  of  the  tension  reinforcements ; 

modulus  of  elasticity  of  tension  reinforcement 

m.  the  ratio  — — : — -r-. » —          — : —  — : — * 

modulus  of  elasticity  of  concrete  in  compression 

To  calculate  the  position  of  the  neutral  axis  in  the  beams  experimented  on,  it 
is  necessary  to  introduce  the  value  of  m  appropriate  to  the  concrete  employed. 

The  mean  value  of  the  modulus  of  elasticity  of  a  test  prism  made  of  the  same 
concrete  was  equal  to  3 -41  X  106  Ibs.  per  inch2  when  the  compression  was  between 
570  and  1,420  Ibs.  per  square  inch,  as  these  were  stresses  approximately  marking 
the  second  phase  of  the  bending  in  question.  The  modulus  of  elasticity  of  the  steel 
was  known  to  be  32*5  X  106  Ibs.  per  square  inch,  m  therefore  had  the  value  9 -5. 

Table  No.  26  affords  a  comparison  of  the  positions  of  the  neutral  axis  as  observed 
and  as  calculated  for  the  various  percentages  and  for  the  variations  of  bending 
moment  set  out  in  the  Table. 

TABLE  No.   26. 


Distance  from  the  Neutral  Axis  to 

2  Reference 

Percentage  of 

Variations  of  the  Bending 

the  Centres  of  the  Reinforcements. 

i      .  j 

Mpl-fll 

TV1"                            J_ 

Actual 

Calculated. 

Foot-tons. 

Inches. 

Inches. 

G. 

0-50 

7-56    to    13-05 

10-709 

10-630 

F. 

0-98 

7-56    to    14-90 

9-134 

9-410 

A.B. 

1-94 

7-56    to    16-73 

7-795 

7-953 

C.D.  (slit) 

3-14 

8-83    to    19-40 

6-614 

6-772 

1  This  formula  applies  where  there  are  tension  reinforcements  only. 

2  See  Table  No.  12,  pp.  32,  38,  for  particulars  of  beams. 


R.C. 


98 


REINFORCED   CONCRETE 


It  is  seen  that  the  results  of  experiment  accord  closely  with  the  values  calcu- 
lated according  to  the  hypothesis  of  the  conservation  of  plane  sections  applied  to 
the  phase  in  which  the  tension  is  zero,  and  that  even  for  a  beam  cut  by  a 
transverse  fissure  and  notwithstanding  the  slipping  of  the  reinforcements. 

4°.  Law  of  Deformation  of  Reinforced  Concrete. 

Table  No.  27  shows  the  results  of  some  calculations  made  on  one  of  the  beams 
to  verify  the  law  of  deformation  obtained  by  the  direct  tension  tests. 

The  bending  moments  applied  to  the  beam  are  given  in  column  1.  The 
elongations  of  one  of  the  reinforcements,  which  were  measured  directly  and 
without  possibility  of  error,  are  given  in  column  2  ;  in  column  3  the  unital  stress 
obtained  by  multiplying  the  observed  strain  by  the  modulus  of  elasticity  of  the 
metal,  32-4  X  106  Ibs.  per  square  inch  ;  and  in  column  4  the  total  tension  supplied 
by  the  reinforcements,  the  area  of  which  was  2 '4  sq.  ins.  In  column  5  the  distance 
from  the  centre  of  the  reinforcements  to  the  centre  of  compression,  determined 
from  the  calculated  position  of  the  neutral  axis,  is  given.  In  column  6  the 
moments  of  resistance  obtained  by  multiplying  the  figures  of  column  4  by  those 
of  column  5  are  given. 

By  subtracting  the  moment  of  resistance  due  to  the  reinforcement  from  the  total 
applied  bending  moment,  the  moment  of  resistance  due  to  the  tensions  in  the 
concrete  is  obtained.  These  are  given  in  column  7. 


TABLE  No.   27. 


1 

2. 

3. 

4. 

0. 

6. 

7. 

"Variations  of  Tension  of 

Variations  of  Moment 

Total 
Applied 

Percentage 

the  Reinforcement. 

of  Resistance. 

Bending 

Elongation  of 

Lever  Arm. 

Moments. 
(Foot-tons.) 

Reinforcement. 

Tons  per 
Square  Inch. 

Total  Tons. 

Ins. 

Due  to 
Metal. 

Due  to 
Concrete 
in  Tension. 

Foot-tons. 

Foot-tons. 

3-43 

0-00365 

0-53 

1-26 

11-496 

1-21 

2'22 

7-09 

0-01030 

1-49 

3-59 

11-811 

3-54 

3-56 

12-60 

0-02725 

3-95 

9-47 

12-126 

9-58 

3-03 

18-08 

0-04350 

6-10 

14-63 

12-165 

14-85 

3-24 

Similar  results  were  found  in  the  cases  of  the  other  beams  tested. 

It  will  be  observed  that  the  moment  of  resistance  produced  by  the  stretched 
concrete  increases  at  first  very  rapidly  so  long  as  the  deformation  is  small.  After 
attaining  a  maximum  value  it  diminishes  slightly,  and  thereafter  remains  sensibly 
constant.  These,  facts  agree  well  with  the  inferences  drawn  from  the  direct  tension 
tests.  In  bending,  there  is  not  observed  immediately  beyond  the  limit  of  elasticity 
the  transient  augmentation  of  resistance  noticed  in  the  direct  tension  tests.  This  is 
explained  by  the  fact  that  the  various  layers  of  concrete  in  tension  are  not  equally 
elongated  at  the  same  instant ;  in  fact,  most  of  the  layers  are  not  stressed  at  all 
beyond  the  tension  at  which  the  modulus  of  elasticity  becomes  constant. 


ANALYSIS   OF   BENDING  EXPERIMENTS  99 

The  final  moment  of  resistance  of  3-24  foot-tons  supplied  by  the  concrete 
corresponds  to  a  tension  of  about  135  Ibs.  per  square  inch.  This  is  the  increase  in 
tension  caused  by  the  mechanical  test,  and  is  additional  to  the  initial  tension 
resulting  from  the  presence  of  the  reinforcements.  This  latter  tension  might  be 
put  at  213  Ibs.  per  square  inch.  Thus  the  total  tension  of  the  concrete  during 
bending  after  the  limit  of  elasticity  had  been  passed  would  be  about  350  Ibs. 
per  square  inch,  and  would  be  constant  at  this  figure. 

5°.  Adhesion  and  Slipping  of  the  Reinforcements. 

From  the  experiments  of  the  Commission  this  very  conspicuous  fact  emerges, 
that  the  extremities  of  the  reinforcements  are  not  sensibly  displaced  relatively  to 
the  concrete  before  the  adhesion  had  been  completely  destroyed  elsewhere,  and  also 
that  in  the  neighbourhood  of  the  application  of  concentrated  loads  there  were 
important  relative  displacements. 

Three  different  phases  of  the  phenomenon  united  by  short  periods  of  transition 
were  clearly  marked  in  the  bending  experiments  recorded  on  pp.  32,  38. 

In  the  first,  which  extended  to  a  bending  moment  of  about  11 '30  foot-tons  and 
to  a  slipping  of  the  reinforcement  of  0*00113  per  cent.,  the  displacement  of  the 
reinforcement  was  small  and  increased  proportionately  to  the  load. 

In  the  second  phase,  comprised  between  bending  moments  of  18  and  29  foot- 
tons  and  between  slippings  of  0'004  per  cent,  and  0*012  per  cent.,  the  slip- 
pings  still  increased  proportionately  to  the  load,  but  with  a  progression  six  or  seven 
times  more  rapid  than  in  the  first  phase. 

Between  these  two  phases  of  rectilinear  displacement  there  is  a  curve  of  tran- 
sition. In  the  third  phase,  which  immediately  preceded  the  failure  of  the  beam 
by  the  destruction  of  the  adhesion  between  the  reinforcements  and  the  concrete, 
the  adhesion  seems  to  have  gradually  "disappeared  outwards  from  the  point  of 
maximum  stress  over  the  whole  length  of  the  reinforcements. 

Omitting  this  last  period  of  doubtful  and  complex  nature,  it  was  found  that  at 
the  end  of  the  second  phase  the  reinforcement  had  slipped  0'012  percent,  relatively 
to  the  concrete  which  surrounded  it. 

The  deformation  of  the  concrete  was  necessarily  the  greater  as  the  reinforce- 
ment was  approached,  and  from  closely  approximate  calculations  the  maximum 
slipping  of  the  concrete  in  contact  with  the  reinforcement  was  about  0'6 
per  cent. 

This  high  figure,  which  would  have  been  rejected  a  priori  as  inadmissible 
before  knowing  the  laws  of  the  deformation  of  the  concrete,  appears  within  the 
bounds  of  probability,  since  it  is  known  that  concrete  might  without  breaking 
undergo  elongations  greater  than  0'2  per  cent,  when  submitted  to  tensions  or 
shortenings  of  2  or  3  per  cent,  when  spiralled  and  compressed. 

This  property  which  concrete  possesses  of  slipping  without  breaking,  appears  to 
play  an  important  role  in  reinforced  pieces  of  permitting  the  distribution  over  great 
lengths  of  intense  shearing  stresses,  which  tend  to  be  produced  on  certain  points  in 
the  neighbourhood  of  concentrated  loads. 

In  a  beam  on  which  the  bending  moment  was  increased  till  cracking  commenced , 
then  removed  and  re-applied  thirty-nine  times,  it  was  found  that,  although  the 
elongations  and  contractions  of  the  concrete  ceased  to  grow,  the  slipping  was 
progressive.  The  load  imposed  on  the  adhesion  of  the  concrete  to  the  reinforce- 
ments in  these  repeated  loadings  thus  exceeded  the  limit  of  elasticity,  and  even, 
it  seemed,  that  of  stability,  although  the  bending  moment  was  only  half  that  of 

H  2 


100  REINFORCED   CONCRETE 

the  moment  which  on  its  first  application  determined  the  slipping  of  the  reinforce- 
ment in  another  identical  beam. 

Considered  by  itself,  this  fact  is  rather  disquieting  ;  but  it  is  known  from  other 
sources  that  beams  in  which  the  adhesion  has  been  highly  stressed  have  supported 
a  great  number  of  repetitions  of  bending  moments  without  the  deterioration  or 
deformation  growing  indefinitely.  A  prism  tested  at  Quhnper  underwent  more 
than  132,000  repetitions  of  a  load  which  stressed  the  adhesion  highly. 

It  would  seem  that  the  maximum  stress  imposed  on  adhesion  by  the  application 
of  a  concentrated  load  is  at  first  localised,  and  that  it  gradually  propagates  itself 
along  the  reinforcement  till  at  no  place  its  value  exceeds  what  the  concrete  can 
carry  without  the  slipping  progressing  indefinitely.  Further  experimental  informa- 
tion however  is  required  on  this  point. 

In  those  beams  tested  up  to  the  point  at  which  slipping  took  place,  an  attempt 
was  made  to  obtain  information  regarding  the  resistance  opposed  to  the  slipping 
of  the  reinforcement  in  bent  pieces,  but  only  indications  without  scientific  precision 
are  obtainable.  In  fact,  the  law  of  the  distribution  of  the  slipping  stresses  was 
ignored  on  the  length  of  the  reinforcements,  and  consequently  no  account  was 
taken  of  the  maximum  values  the  stresses  attained  in  the  most  highly  stressed 
places.  It  was  thus  a  purely  conventional  mode  of  calculation,  to  the  results  of 
which  no  scientific  value  is  attributable,  but  which  may  be  useful  for  the  checking 
of  design  and  the  interpretation  of  the  results  of  experiments. 

If  the  concrete  produced  no  tension,  one  of  the  components  of  the  resisting 
couple  would  be  furnished  solely  by  the  reinforcements,  and  the  slipping  tendency 
of  the  tension  reinforcements  would  be  at  each  point  proportional  to  the  shearing 
effort.  In  the  beams  experimented  on  as  the  loads  were  concentrated  at  about 
3  feet  from  the  abutments,  the  shear  was  constant  between  the  point  of  appli- 
cation of  the  load  and  the  abutment,  and  the  total  slipping  tendency  was  thus 
equal  to  the  maximum  tension  in  the  reinforcement,  so  that  the  slipping  stress 
per  unit  area  of  the  surface  of  the  reinforcements  was  easily  arrived  at. 

In  this  way  a  resistance  to  slipping  of  185  Ibs.  per  square  inch  was  found  for 
the  beam  with  four  bars  each  0'874  inch  diameter,  and  213  Ibs.  per  square  inch 
for  the  beam  with  two  bars  each  1'57  inches  diameter.  In  both  cases  the  reinforce- 
ments were  placed  in  the  folds  of  vertical  sheet-iron  stirrups.  An  examination  of 
the  cracks  led  in  both  cases  to  the  view  that  the  displacement  of  the  reinforce- 
ments may  not  have  taken  place  by  the  failure  of  the  resistance  to  slipping 
properly  so  called,  but  by  the  dislocation  of  the  bed  of  concrete  covering  the 
reinforcements. 

From  experiments  made  by  M.  Mesnager  on  the  tearing  and  driving  of  rods 
from  cubes  of  concrete,  values  of  from  190  to  235  Ibs.  per  square  inch  were 
obtained,  cracking  of  the  concrete  preceding  or  accompanying  failure  by  slipping. 

These  facts  show  clearly  that  the  values  obtained  by  experimenting  with  rods 
buried  in  very  large  blocks  of  concrete  which  have  shown  resistances  as  high  as 
640  Ibs.  per  square  inch  cannot  be  applied  to  the  case  of  slipping  in  ordinary 
reinforced  concrete  where  the  section  of  concrete  used  is  never  large  enough  to 
prevent  cracking  before  slipping. 

6°.  Influence  of  Fissures  on  the  Resistance  of  the  Compression  Areas. 

In  order  to  determine  whether  the  hamstringing  that  takes  place  in  beams 
does  not  provoke  the  premature  crushing  of  the  concrete,  two  beams  were  manu- 
factured with  an  artificial  fissure  extending  across  65  per  cent,  of  the  section. 


ANALYSIS   OF    BENDING   EXPERIMENTS  101 

With  a  view  to  causing  rupture  by  crushing  of  the  concrete,  the  reinforcement 
consisted  of  two  1'57  inches  diameter  rods,  giving  the  abnormal  percentage  of  3'14. 

The  beams,  however,  collapsed  by  the  slipping  of  the  reinforcements,  and  the 
only  inference  that  could  be  drawn  was  that  the  compression  in  the  concrete  at  the 
moment  of  collapse  was  not  the  maximum  compression  that  might  have  been 
resisted.  Assuming  all  the  tension  required  was  furnished  by  the  reinforcements, 
the  mean  compression  on  the  compression  area  was  about  1,250  Ibs.  per  square  inch. 
If  the  elasticity  had  remained  constant,  and  consequently  the  distribution  of  stress 
linear,  the  maximum  intensity  of  stress  would  have  been  2,500  Ibs.  per  square  inch. 
The  elasticity,  however,  is  reduced,  but  nevertheless  the  maximum  stress  should  not 
be  evaluated  at  less  than  1,850  Ibs.  per  square  inch. 

The  resistance  to  direct  crushing  of  blocks  of  the  same  concrete  not  reinforced 
did  not  exceed  2,000  Ibs.  per  square  inch.  It  would  seem,  therefore,  that  the 
fissuring  which  occurs  in  the  sagging  of  bent  prisms  does  not  hasten  in  an 
appreciable  manner  the  crushing  of  the  part  of  the  concrete  subject  to 
compression. 

This  fact  is  perhaps  explained  by  the  ductility  that  concrete  presents  from  the 
point  of  view  of  slipping,  and  by  the  help  derived  by  the  compressed  areas  from 
the  increased  resistance  to  transverse  swelling  which  precedes  crushing. 

C.  Effects  of  Transverse  Bemforcements. 
1°.  Bending  Experiments. 

The  opinion  has  been  expressed  that  in  consequence  of  the  inequality  of  the 
limits  of  elasticity  which  concrete  presents  after  it  has  been  submitted  to  tension 
or  to  compression,  shear  ought  to  produce  a  transverse  swelling  which  would  put 
a  tensile  stress  on  the  vertical  reinforcements,  and  thereby  allow  them  to 
produce  a  useful  effect  in  resisting  the  shear  of  the  concrete. 

In  order  to  obtain  information  on  this  question  the  experimental  method  was 
resorted  to.  Measuring  apparatuses  were  placed  vertically  on  the  lateral  faces  of 
two  of  the  beams,  with  the  usual  vertical  reinforcements.  In  one  case  the  swelling 
was  only  0'005  per  cent.,  which  represented  a  mean  stress  in  the  stirrups  of  about 
0'6  ton  per  square  inch.  In  another,  in  which  failure  took  place  by  shearing,  the 
swelling  did  not  exceed  O'Ol  per  cent,  before  the  appearance  of  cracks,  which 
indicates  at  the  most  a  tension  of  1*4  tons  per  square  inch  of  the  vertical 
reinforcements. 

The  measuring  apparatuses  were  placed  in  vertical  planes  equally  distant  from 
the  support  and  the  point  of  application  of  the  load,  where  the  beam  resisted  both 
the  maximum  shear  and  a  considerable  bending  moment.  In  the  height  of  the 
beam  on  which  measurements  were  made,  there  was  comprised  both  tension  and 
compression  areas,  so  that  the  variation  ascertained  in  the  total  height  would 
result  from  the  superposition  of  the  effects  of  shearing  in  the  whole  section  on 
the  vertical  contraction  in  the  tension  area,  and  on  the  vertical  swelling  on  the 
compression  area.  It  is  thus  certain  that  if  the  resultant  vertical  deformation  in 
the  whole  depth  of  the  beam  was  a  swelling  in  the  tension  area,  it  was  much  less 
than  the  mean,  consequently  the  help  derived  from  the  tension  in  the  stirrups  in  this 
portion  must  have  been  very  small.  On  the  other  hand,  the  vertical  reinforce- 
ments have  been  able  to  furnish  really  important  tensions  in  the  compression  areas, 
and  consequently  assist  the  lateral  strength  of  the  concrete. 

When  one  recalls  that  it  is  in  the  tension  area  that  oblique  cracking  due  to 


*  \ 

;/-w 

102  REINFORCED   CONCRETE 

shear  commences,  and  that  it  is  the  longitudinal  reinforcements  which  resist 
slipping,  one  is  led  to  the  conclusion  that  so  long  as  the  concrete  is  not  cracked 
the  stirrups  hardly  act  by  tension. 

Theoretical  considerations  indicate  that  so  long  as  the  limit  of  elasticity  is  not 
passed,  these  stirrups  hardly  assist  the  shear,  but  the  action  thereafter  assumes  a 
great  importance ;  in  fact,  well-placed  stirrups  may  prevent  the  ruin  of  a  structure 
after  the  concrete  is  completely  cracked. 

2°.   Torsion  Experiments. 

The  experiments  above  referred  to  attempted  to  elucidate  directly  the  role  of 
the  transverse  reinforcements  in  bent  pieces,  but  no  information  was  obtainable 
from  them  on  the  characteristic  effects  of  pure  shear.  To  this  end  M.  Mesnager 
devised  the  torsion  tests  described  on  p.  27. 

It  was  established  that  under  a  moment  of  torsion  equal  to  one-half  the  breaking 
moment  the  elongation  of  the  reinforcements  was  only  such  as  produced  a  stress  of 
about  0'60  ton  per  square  inch,  and  although  it  is  the  case  that  shearing  produces 
a  lateral  swelling  of  the  concrete,  it  is  so  slight  as  to  merit  attention  only  under 
very  heavy  loads. 

The  vertical  deformations  produced  by  shearing  add  themselves  to  those 
resulting  from  the  swelling  of  the  concrete  in  the  compression  areas,  and  in 
consequence  the  reinforcements  perpendicular  to  the  axis  there  give  tensions  which 
increase  the  resistance  to  shear  and  to  compression. 

In  the  tension  areas  the  transverse  variations  in  volume  produced  by  shear  and 
by  bending  oppose  each  other,  the  effect  of  the  former  predominating  at  the 
supports,  and  of  the  latter  at  the  places  where  the  bending  moment  is  a  maximum. 

D.  Resistance  of  Reinforcements  to  Shear. 

It  is  known  that  in  imperfectly  supervised  work,  and  there  is  always  some 
such,  the  adhesion  fails  occasionally  between  the  ribs  executed  at  first  and  the 
slabs  executed  later.  It  should  be  provided  that  the  reinforcements  traversing 
any  such  plane  of  separation  should  in  themselves  be  sufficient  to  resist  the  whole 
of  the  horizontal  slipping  tendency. 

The  resistance  of  these  reinforcements  is  complex,  and  comprises  in  the 
simplest  case,  which  is  that  of  vertical  reinforcements,  two  elements — viz.,  the 
resistance  of  the  metal  to  shear  and  the  friction  developed  between  the  surfaces 
in  contact.  The  last  element  is  extremely  variable,  and  in  order  to  keep  it  as 
uniform  a  quantity  as  possible  during  the  experiments,  the  sub-Commission  has 
prevented  adhesion  by  interposing  sheets  of  oiled  paper.  These  experiments  are 
described  on  pp.  25,  26. 

It  is  observed  that  whilst  the  percentages  employed  are  nearly  equal  in  order 
to  equalise  the  tensions  produced  by  the  setting  of  the  concrete,  and  consequently 
the  friction  developed  between  the  surfaces  of  the  concrete,  the  forms  and 
dimensions  of  the  reinforcements  are  very  various. 

The  experiments  have  established  the  important  fact  that  the  resistances 
obtained  relatively  to  the  section  of  the  metal  have  been  sensibly  proportional  to 
the  characteristic  resistance  of  the  metal ;  or,  in  other  words,  the  shearing  resistance 
was  sensibly  proportional  to  the  area  of  the  reinforcement  and  independent  of  its 
form. 

The  qualities  of  both  elements  in  the  test  cube  influence  the  strength  of  the 


ANALYSIS   OF   BENDING  EXPERIMENTS  103 

whole,  and  one  easily  grasps  the  mechanism  of  this  influence  in  examining  the  results 
of  experiments. 

The  concrete  crushed  near  the  surfaces  of  slipping  and  the  reinforcements 
took  the  form  indicated  in  Fig.  29.  They  resisted  thus  not  by  shear  alone,  but 
by  shear  combined  with  bending  to  a  short  radius. 

It  is  thus  possible  that  the  resistance  of  the  reinforcements  depends  on  the 
extent  of  the  zone  of  crushing  and  on  the  quality  of  the  concrete.  The  results 
obtained  apply  only  to  concrete  containing  6  cwts.  of  cement  to  14*35  cubic 
feet  of  sand  and  2  8 '7  cubic  feet  of  gravel. 

The  graphic  representation  of  the  results  obtained  by  measuring  carefully  the 
relative  displacements  of  the  two  surfaces  of  contact  indicates  a  point  analogous 
to  the  elastic  limit,  beyond .  which  the  displacements  grow  considerably.  This 
point  is  at  a  stress  of  about  8  tons  per  square  inch  of  the  section  of  the 
reinforcements,  and  the  maximum  load  supported  varied  between  11*5  and  16 '5 
tons  per  square  inch  of  the  cross 
section  of  the  reinforcements.  j 

These  figures  indicate  the  effect 
of  the  quality  of  the  concrete.  Had 
the  concrete  been  of  sufficient  quality 
to  entirely  prevent  crushing,  the 
reinforcements  would  have  developed 
the  ordinary  resistance  to  shear.  It 
is  possible  that  the  percentage  of 
reinforcement  used  was  a  little  too 
high  for  the  quality  of  the  concrete. 

It  is  important  to  remark  that 
the  resistances  obtained  would  not 
have  been  so  large  if  the  rods  had 
been  nearer  the  surface  of  the  con- 
crete, as  the  thin  covering  would 
have  been  more  easily  burst. 

No  experiment  has  been  made  on  the  resistance  which  proceeds  from  friction 
on  the  surface  of  slipping.  The  coefficient  of  friction  of  concrete  on  concrete 
lies  between  0*60  and  0*75,  so  that  the  resistance  given  by  friction  might  attain 
those  proportions  of  the  tension  resistance  of  the  reinforcement.  It  would  not  be 
advisable  to  add  the  whole  or  the  greater  part  of  this  resistance  to  the  bending- 
shear  resistance  due  to  the  metal,  because  it  is  known  that  the  superposition  of 
different  stresses  on  metal  hastens  its  rupture. 

E.  Experiments  on  Ribbed  Slabs. 

The  propriety  of  the  application  of  the  hypothesis  of  the  conservation  of  plane 
sections  during  bending  and  of  the  exactitude  of  the  formulae  which  give  the 
position  of  the  neutral  axis  in  rectangular  pieces  subjected  to  bending  has  been 
discussed  on  pp.  78,  79.  A  research  was  carried  out  on  two  ribbed  T  slabs  with 
a  view  to  finding  out  whether  the  same  hypothesis  and  formulae  applied  in  that  case. 

Precautions  were  taken  to  eliminate,  as  far  as  possible,  merely  local  warpings 
or  irregularities,  and  to  obtain  a  record  of  the  deformations  of  the  structure  as  a 
whole. 

The  salient  feature  of  the  results  is  their  striking  regularity,  as  plotted 
graphically  on  p.  47. 


104  REINFORCED    CONCRETE 

The  uniformly  distributed  load  which  the  first  slab  could  carry  without  stressing 
the  reinforcements  beyond  6'3  tons  per  square  inch  was  about  6 '4  tons.  Up  to  this 
load,  the  deformations  were  sensibly  plane.  Beyond  it,  however,  slight  deviations 
were  observed.  In  the  second  slab  the  load  was  applied  by  means  of  a  balanced 
platform  to  the  upper  surface  of  the  slab  immediately  over  the  rib.  The  defor- 
mations were  perfectly  uniform  for  loads  up  to  9  tons ;  but  beyond  that  load, 
and  largely  exceeding  the  load  which  would  be  applied  in  practice  to  a  similar 
slab,  plane  sections  showed  sensible  warpings  in  the  opposite  sense  to  those 
observed  in  the  first  slab. 

Comparing  these  results  with  those  of  the  tests  made  on  the  floors  constructed 
at  the  Paris  Exhibition,  the  conclusion  may  safely  be  drawn  that  in  ribbed  slabs 
plane  sections  remain  plane  during  bending,  any  deviation  from  the  plane  being 
of  so  slight  magnitude  as  not  to  merit  attention. 

The  determination  of  the  position  of  the  neutral  axis  in  any  structure  is  the 
key  to  the  correct  calculation  of  the  stresses  in  the  concrete  and  moment  of 
resistance  of  the  member. 

The  measurements  taken  on  the  slab  4  feet  wide  show  that  the  neutral  axis 
occupied  a  position  2 '24  inches  below  the  upper  surface  of  the  slab.  In  the  slab 
6  feet  6  inches  wide  the  neutral  axis  was  lower  under  light  loads,  but  afterwards 
rose  to  and  retained  till  the  end  of  the  experiment  a  position  sensibly  identical 
to  that  in  the  first  slab.  The  ratio  x  of  the  distance  of  the  centre  of  gravity  of 
the  tension  reinforcements  from  the  neutral  axis,  to  its  distance  from  the  upper 
surface  of  the  slab,  is  thus  0'70,  and  assuming  the  efficient  width  of  the  slab  to  be 
90  per  cent,  of  its  total  width,  and  putting  in  the  known  data  in  the  expression 
given  on  p.  97  for  the  value  of  x  the  value  of  m,  the  ratio  of  the  coefficients 
of  elasticity  of  steel  and  concrete  is  found  to  be  10'9.  From  this  figure  and  from 
the  known  coefficient  of  elasticity  of  the  steel  used,  the  modulus  of  elasticity  of  the 
concrete  is  calculated  at  1,270  tons  per  square  inch. 

The  modulus  of  elasticity  of  this  concrete  was  also  obtained  experimentally 
by  the  compressive  tests  of  two  prisms,  the  mean  values  up  to  a  stress  of  1,420  Ibs. 
per  square  inch  being  1,274  and  1,175  tons  per  square  inch  respectively. 

The  experiment  in  question  has  thus  verified  as  exactly  as  possible  the  formula 
which  determines  the  position  of  the  neutral  axis,  and  which  translates  algebraically 
the  hypothesis  of  the  conservation  of  plane  sections  and  of  the  constancy  of 
the  tension  in  the  area  submitted  to  elongation. 

Participation  of  Slabs  in  the  Resistance  of  the  Ribs. 

The  deformations  were  measured  not  only  in  the  ribs,  but  in  the  slabs  at  points 
removed  from  the  ribs,  and  it  was  found  that  in  the  slab  4  feet  wide  the  neutral 
axis  rises  higher  in  the  slab  the  further  away  from  the  rib  the  measurement  is 
taken.  That  is,  of  course,  as  is  to  be  expected,  since  the  slab  acts  in  two  ways — 
viz.,  as  a  part  of  the  compression  area  of  the  rib  and  as  an  independent  beam,  and 
in  proportion  as  the  latter  action  preponderates  the  neutral  axis  rises,  in  order  that 
the  necessary  tension  resistance  may  be  obtained. 

The  neutral  axis  remained  sufficiently  close  to  the  lower  surface  of  the  slab 
throughout  the  test  that  the  tension  was  neglected,  and  account  only  taken  of  the 
compressions  in  the  calculation  of  the  resistance  of  slab  and  rib.  Now,  what- 
ever the  value  of  the  coefficient  of  elasticity,  these  compressions  are  proportional 
to  the  products  obtained  by  multiplying  the  thickness  of  the  slab  situated  above 
the  neutral  axis  by  the  shortening  of  the  upper  fibre  of  the  slab. 


STRESSES   DUE   TO   SETTING 


105 


The  sections  in  which  the  three  apparatuses  were  placed — viz.,  on  the  axis  of 
the  rib,  at  13-40  inches  and  at  22-44  inches  from  it — gave  products  in  the  ratio 
21,  20  and  17'6  respectively.  The  geometric  mean  of  these  figures  is  19. 

Consequently  in  the  slab  in  question,  in  which  the  ratio  of  width  of  slab  to 
span  was  0'42,  the  slab  gave  Jy  —  0'90  of  the  resistance  it  would  have  furnished 
if  in  all  its  width  it  had  been  absolutely  rigid  with  the  rib.  So  that  to  calculate 
the  resistance  of  this  floor  one  might  consider  the  slab  as  entirely  solid  in  the 
deformation  of  the  rib  on  condition  of  taking  account  of  only  0'90  of  its  width. 

In  the  slab  6  feet  wide  the  ratio  of  breadth  to  span  attains  the  exceptional 
figure  of  0'70,  and  by  making  the  above  assumptions — which  do  not  apply  with  so 
great  accuracy  in  this  case  as  in  the  former — the  participation  of  the  slab  in  the 
resistance  of  the  rib  was  0'55  of  what  it  would  have  been  in  the  case  of  absolute 
solidarity. 

To  determine  as  a  function  of  the  span  taken  as  unity  the  effective  widths  of 
the  slabs  corresponding  to  spacing  of  beams  of  0'40  and  0*70,  it  is  necessary  to 
multiply  these  figures  respectively  by  0'90  and  0*55.  The  products  0-36  and 
0-385  are  thus  obtained.  These  results  appear  somewhat  anomalous,  as  it  is 
improbable  that  the  useful  effect  of  a  slab  increases  only  in  the  slight  proportion 
of  0*36  to  0'385  when  its  width  grows  in  the  proportion  of  0'40  to  0-70,  although 
it  should  be  remarked  that  the  influence  of  secondary  bendings  rapidly  becomes 
more  important  with  the  increase  in  width. 

One  is  led  to  the  conclusion  by  the  consideration  of  these  and  of  other 
experiments  that,  when  the  width  of  the  slab  is  0'40  of  the  span,  its  effective 
width  may  be  taken  about  90  per  cent,  of  its  total  width,  and  that  the  help  it 
gives  the  rib  grows  more  and  more  slowly  as  the  width  of  the  slab  becomes 
greater. 

F.  Variations  in  Length  of  Bars  of  Metal  Buried  in  Concrete  during  Setting. 

On  p.  23  the  experiments  carried  out  to  throw  light  on  the  above  question 
are  described. 

Table  No.  28  gives  the  results  found. 

TABLE  No.  28. 


Pieces  kept  in  Water. 

Pieces  kept  in  Air. 

Percentage. 

Tension  in  the 
Metal. 

Compression  in 
the  Concrete. 

Compression  in 
the  Metal. 

Tension  in  the 
Concrete. 

Tons  per  square 

Lbs.  per  square 

Tons  per  square 

Lbs.  per  square 

inch. 

inch. 

inch. 

inch. 

0-23 

1-40 

7-1 

2-51 

12-8 

0-49 

1-40 

15-2 

1-95 

21-3 

1-00 

1-27 

28-5 

1-68 

37-5 

1-44 

1-12 

36-0 

1-68 

54-0 

1-96 

1-12 

49-0 

1-68 

73-0 

2-96 

1-12 

57-0 

1-68 

111-0 

4-00 

1-27 

114-0 

— 

— 

4-93 

1-12 

123-0 

1-68 

185-0 

9-00 

1-27 

256-0 

1-40 

282-0 

106  REINFORCED   CONCRETE 

It  is  seen  that  for  cylinders  kept  in  air  there  were  found  compressions  in  the 
metal  Avhich  attained  in  the  length  of  19*68  inches  a  value  of  2-51  tons  per 
square  inch  for  a  percentage  of  0*23,  1*95  tons  per  square  inch  for  a  percentage 
of  0-49,  and  which  starting  from  TO  per  cent,  up  to  9  per  cent,  remained  sensibly 
constant  and  in  the  neighbourhood  of  1*68  tons  per  square  inch.  The  tension  in 
the  concrete  balancing  the  above  has  varied  almost  proportionately  to  the  per- 
centage from  12  to  280  Ibs.  per  square  inch. 

In  the  prisms  kept  in  water  the  reinforcements  took  tensions  almost  independent 
of  the  percentage  of  reinforcement  and  of  about  1*2  tons  per  square  inch,  whilst  the 
opposing  compression  in  the  concrete  varied  from  7  to  256  Ibs.  per  square  inch. 

The  experiments  appear  to  establish  the  surprising  fact  that  when  the  per- 
centage of  metal  exceeds  1  per  cent,  an  increase  in  percentage  has  no  sensible 
effect  on  the  stresses  set  up  in  the  reinforcement  as  a  result  of  the  setting  of  the 
concrete,  and  that  the  corresponding  stresses  in  the  concrete  are  quasi  proportional 
to  the  percentage,  whatever  its  value. 

The  experiments  just  described  cannot  be  considered  applicable  to  large  pieces. 
Since  the  production  of  the  stresses  depends  on  the  adhesion,  their  values  are 
necessarily  zero  at  the  extremities,  and  so  much  the  greater  on  the  average,  as  the 
pieces  are  longer  in  relation  to  the  transverse  dimensions  of  the  reinforcements  up 
to  a  certain  limit  far  removed. 

Experimental  proof  of  this  can  be  had  by  referring  to  the  internal  stresses 
measured  in  other  pieces — e.g.,  in  the  tension  prisms  6*56  feet  X  3*94  inches  X  3'94 
inches,  the  compression  of  the  reinforcements  was  about  2 -92  tons  per  square  inch. 
In  the  beams  of  13*12  feet  X  15*75  inches  X  7 '8 7  inches,  when  the  concrete 
had  set  freely  and  unloaded  in  air  the  compression  was  about  5'1  tons  per  square 
inch,  and  was  very  much  more  in  the  compression  reinforcements  when  the  concrete 
of  the  beam  set  under  a  heavy  load. 

The  incontestable  result  of  this  series  of  experiments  is  to  demonstrate  that 
to  obtain  figures  applicable  to  structures  concerning  the  effects  of  the 
variations  in  volume  of  concretes  or  mortars,  the  surest  method  is  from  the  results 
of  similar  pieces.  If  smaller  pieces  are  employed,  it  would  be  necessary  to  establish 
between  the  transverse  and  longitudinal  dimensions  of  the  reinforcements 
proportions  analagous  to  those  met  with  in  structures. 

G.  The  Influence  of  the  Proportion  of  Gauging  Water   on   the  Strength  and 

Elasticity  of  Concrete. 

It  is  known  from  experiments  made  elsewhere  that  the  marked  inferiority  of 
very  wet  mortars  and  concretes  diminishes  with  time,  but  the  experiments  of  the 
Commission  show  even  after  ninety  days'  setting  that  the  resistance  and  elasticity 
vary  with  the  proportion  of  gauging  water. 

Compression  tests  after  ninety  days  on  similar  prisms  14*2  inches  X  2*85 
inches  X  2*75  inches,  composed  of  6  cwts.  of  Portland  cement,  14*35  cubic  feet  of 
sand  and  28*7  cubic  feet  of  gravel  were  made. 

The  first  series  were  gauged  with  8*8  per  cent,  by  weight  of  water.  There 
was  obtained  a  resistance  to  crushing  of  1,850  Ibs.  per  square  inch,  and  a  coefficient 
of  elasticity  of  2,000  tons  per  sq.  in.  between  stresses  of  280  to  850  Ibs.  per  square 
inch,  and  1,160  tons  per  sq.  in.  between  1,280  and  1,700  Ibs.  per  square  inch. 

The  second  series  were  gauged  with  11*0  per  cent,  of  water.  A  resistance  of 
710  Ibs.  per  square  inch  was  obtained,  whilst  the  coefficient  of  elasticity  between 
stresses  of  from  140  to  280  Ibs.  per  square  inch  was  1,040  tons  per  sq.  in.,  and 
420  tons  per  sq.  in.  between  stresses  of  from  560  to  710  Ibs.  per  square  inch. 


EFFECT   OF   SHOCKS  107 

H.  Effects  of  Direct  and  Repeated  Shocks  on  the  Adhesion  and 
Resistance  of  Concrete. 

Fears  have  been  expressed  regarding  the  disintegration  of  reinforced  concrete 
in  situations  where  it  is  exposed  to  repeated  and  violent  shocks. 

Several  sleepers  in  reinforced  concrete  were  put  into  operation  in  April,  1893, 
on  the  main  down  line  from  Paris  to  Granville  at  the  entrance  to  Dreux  Station, 
and  remained  there  till  June,  1898.  The  road  was  of  78  Ibs.  per  yard,  double 
headed  rails,  and  the  maximum  speed  at  this  place  about  40  miles  per  hour. 

One  of  the  sleepers  which  had  been  placed  near  a  rail  joint  was  examined  by 
the  second  sub-Commission. 

The  composition  of  the  concrete  was  not  known,  but  from  its  appearance  it 
consisted  of  a  rich  mixture  very  carefully  made. 

The  two  features  under  special  examination  were  the  adhesion  of  the  concrete 
to  the  reinforcements  and  the  resistance  of  the  concrete.  From  both  points  of 
view  the  results  were  remarkable. 

To  measure  the  resistance  of  the  adhesion  parts  of  the  reinforcements  were 
torn  from  the  concrete,  and  gave  very  high  figures,  varying  from  820  to  1,310  Ibs. 
per  square  inch  of  the  surface  of  contact. 

This  whole  resistance  was  not,  of  course,  due  to  adhesion  properly  so  called,  but 
even  making  allowances  for  the  other  resistances,  such  as  that  due  to  the 
straightening  of  the  wires  and  the  purely  frictional  grip  of  the  concrete,  the 
values  are  still  high.  A  careful  examination  of  other  parts  of  the  reinforcements 
showed  that  the  adhesion  was  perfect  throughout. 

The  resistance  of  the  concrete  to  compression  in  3-inch  cubes  without  reinforce- 
ment was  8, 410  Ibs.  per  square  inch. 

It  is  thus  shown  that  a  concrete  sleeper,  without  doubt  exceptionally  good  to 
begin  with,  suffered  no  deterioration  in  five  years'  use.  To  appreciate  the 
importance  of  this  demonstration  account  must  be  taken  of  the  great  rapidity 
with  which  the  effects  of  shock  diminish  as  the  distance  from  the  point  of  impact 
increases  if  the  transmission  of  the  stresses  is  not  made  by  absolutely  rigid  and 
continuous  pieces. 

There  is  thus  a  considerable  difference  between  the  sleepers  which  receive 
directly  the  shocks  from  the  chairs  and  the  floor  girders,  and  a  fortiori  the  main 
girders  to  which  the  shocks  are  transmitted  indirectly,  at  least  in  large  works. 
Where  ballast  is  used  this  difference  is  considerably  augmented. 

The  experiment  of  Dreux  should  remove  all  apprehension  for  the  duration  and 
conservation  of  bridges  or  viaducts  carrying  roadways  or  railways. 


APPENDIX 

PAKT  I 

YEETICALLY  IMPOSED  LOADS  AND  .WIND  LOADS  ON  METALLIC  BKIDGES 
AS  DEFINED   IN  THE  EEGULATIONS   OF   AUGUST  29,    1891 l 

VERTICALLY  IMPOSED  LOADS. 
•  Bridges  on  Railways  of  Normal  Gauge. 

The  type  train  will  consist  of  two  engines  with  their  tenders  at  the  head  of  a  train 
of  loaded  waggons,  and  will  have  the  following  weights  and  dimensions : — 


— 

Engine. 

Tender. 

Waggons  (Loaded). 

Number  of  axles       .         ... 

4 

2 

2 

Load  per  axle  (tons) 

13-88 

11-82 

7-88 

Distance    from    leading    buffer   to 

first  axle  (feet)       .... 

8-52 

6-56 

4-92 

Spacing  of  axles  (feet) 
Distance  of    rear  buffer  from    last 

>  3-94 

8-20 

9-84 

axle  (feet)      ..... 

8-52 

6-56 

4-92 

Total  weight  (tons)  .... 

55-52 

23-63 

15-75 

Total  length  (feet)     . 

28-86 

21-32 

19-68 

The  engines,  with  their  tenders,  will  be  placed  at  the  head  of  the  train,  and  the 
maximum  stress  in  each  member  will  be  taken  as  the  maximum  stress  in  it  produced  by 
any  possible  position  of  the  type  train  on  the  bridge.  For  floor  members,  the  stresses 
due  to  an  isolated  axle  load  of  19'69  tons  will  be  taken  as  the  maxima  if  they  are  greater 
than  those  produced  by  the  type  trains. 

Stresses  allowed ;  nett  area  in  tension  or  gross  area  in  compression  : 

For  mild  steel  in  main  girders  over  100  feet  span      =     7 -3  tons  per  square  inch. 
For  other  girders  .  .  .  .  .       =     5-4  do. 

For  rail  bearers  and  cross  girders  .  =     4-76  do. 

For  web  bracing  exposed  to  alternating  stresses      =     3*81  do. 

Bridges  on  Raihuays  of  Metre  (3*28  Feet]  Gauge  and  Over. 

The  weight  per  engine  axle  is  reduced  to  3*00  tons  X  L,  where  L  is  the  gauge  in 
feet.  The  dimensions  of  the  engines  and  the  weights  and  dimensions  of  the  waggons 
will  be  the  same  as  for  normal  gauge,  and  the  tenders  will  be  supposed  to  have  the  same 
weights  and  dimensions  as  the  loaded  waggons. 

For  the  calculation  of  the  stresses  under  a  single  axle  load,  a  weight  of  4*2  tons  X  L, 
where  L  is  the  gauge  in  feet,  shall  be  taken. 


1  "K&istance  des   Materiaux"  (Vol.  L,  p. 
Publics  ;  publishers,  Dunod  et  Pinat,  Paris. 


595),  Bibliotheque  du  Conducteur  de   Travaux 


110  APPENDIX 

Road  Bridges. 

The  stresses  in  each  member  must  not  exceed  the  limits  above  specified  when  either— 
(a)  a  uniformly  distributed  dead  load  of  82  Ibs.  per  square  foot  occupies  the  whole 

platform  of  the  bridge,  including  the  footpaths ;  or 

(&)  as  many  continuous  files  of  tumbrils  as  the  width  of  the  roadway  will  hold,  the 

footpaths  remaining  loaded  with  a  dead  load  of  82  Ibs.  per  square  foot.     Each  tumbril 

to  have  one  axle  and  to  be  drawn  by  two  horses,  all  of  the  following  weights  and 

dimensions :  — 

Tumbrils.     Weight     ......  .         5-91  tons. 

Length,  not  including  the  shafts  .  .  .9-68  feet. 

Width  of  roadway  occupied        .  .  .  .7*26  feet. 

Width  of  wheel  track     .  .  .  .  .4-98  feet. 

Horses.          Weight    .  .  .  .  .  .  .0-69  tons. 

Length  to  each  horse,  including  harness  and  shafts     .         8-20  feet. 

It  must  be  shown  that  the  stress  in  each  member  will  not  exceed  by  more  than 
0'64  ton  per  square  inch  the  limits  fixed  for  railway  bridges,  when  a  vehicle  with  one 
axle  weighing  10 '83  tons,  and  having  the  same  dimensions  as  the  above  tumbrils,  but 
drawn  by  five  horses,  is  substituted  for  one  of  the  tumbrils,  and  also  in  the  case  where 
the  tumbrils  are  replaced  over  the  whole  platform  of  the  bridge  by  waggons  with  two 
axles  drawn  by  four  pairs  of  horses,  having  the  following  weights  and  dimensions  : — 

Waggons.     Weight  on  each  axle        .  .  .  .  7 '88  tons. 

Length  of  vehicle  .  .  .  .       19-68  feet. 

Width  of  track    .  .  .  .  .  .5-58  feet. 

Spacing  of  axles  .  .  .  .  .9-84  feet. 

Distance  of  front  axle  to  front  of  waggon  .  .         4-92  feet. 

Distance  of  rear  axle  to  back  of  waggon  .  .         4 '92  feet. 
Width  of  roadway  occupied       .  7  '38  feet. 

Horses.          Weight  of  a  pair  .....         1'38  tons. 

Length  of  a  pair,  including  harness  and  shafts  .         8 '20  feet. 

Where  the  roads  are  steep  and  the  loading  defined  above  is  not  considered  possible, 
either  at  present  or  in  the  future,  the  loads  to  be  provided  for  may,  with  the  consent  of 
the  Administration,  be  modified,  but  in  no  case  will  they  be  reduced  below  62  Ibs.  per 
square  foot  for  the  dead  load,  and  half  the  above  live  loads. 

Bridges  Carrying  Canals. 

These  must  be  able  to  carry  the  load  of  water  corresponding  to  the  normal  water 
level,  increased  by  12  inches,  without  the  stress  exceeding  in  any  part  the  above  limits. 

WIND  PBESSURE. 
Railway  Bridges. 

The  stress  in  the  metal  under  the  influence  of  the  highest  winds  shall  not  exceed  by 
more  than  0*64  ton  per  square  inch  the  maximum  stresses  already  stated. 

The  maximum  wind  pressure  will  be  taken  at  55  Ibs.  per  square  foot ;  but  it  may 
be  assumed  that  the  passage  of  trains  will  be  suspended  when  the  pressure  exceeds 
35  Ibs.  per  square  foot. 

It  will  be  assumed  that  the  maximum  pressure  will  be  exercised  on  the  nett  surface, 
after  deduction  of  openings,  of  each  of  the  main  girders ;  that  it  will  be  applied  to  the 
total  nett  surface  of  the  windward  girder  of  each  span  ;  and  that  the  wind  pressure 
applied  to  the  total  "uett  surface  of  the  adjacent  main  girder  screened  by  the  first  will  be 
reduced  in  the  ratio  of  the  nett  surface  of  the  first  to  the  total  surface  bounded  by  its 
contour ;  and,  further,  if  there  be  more  than  two  main  girders  on  each  span,  the  effect  on 
the  others  will  be  considered  negligible.  For  metallic  piers  it  will  be  assumed  that  the 
pressure  will  be  exercised  to  the  full  extent  on  the  nett  surface  of  all  members. 

In  considering  the  hypothesis  of  a  train  on  the  bridge,  its  vertical  nett  surface  will  be 
reckoned  as  a  rectangle  9*84  feet  high,  its  lower  edge  T64  feet  above  the  rail  and  extending 


APPENDIX  111 

the  full  length  of  the  bridge.  From  the  area  of  this  rectangle  will  be  dedacted  the  nett 
area  of  the  windward  girder,  and  it  will  be  supposed  that  the  wind  action  on  the  girder 
to  leeward  of  the  train  is  zero. 

It  must  be  shown  that  the  tendency  to  transverse  slipping  and  the  upsetting  action 
of  the  wind  on  bridge  platforms  and  piers,  assuming  the  train  defined  above  to  consist  of 
empty  waggons,  and  taking  into  account  any  special  circumstances  connected  with  the 
structures,  cannot  attain  dangerous  values. 

Road  Bridge*. 

The  above  methods  of  calculation  must  also  be  applied  to  road  bridges,  with  the 
exception  that  no  account  need  be  taken  of  the  presence  of  vehicles  on  the  bridge. 

Bridges  Carrying  C-i-nals. 

A  wind  pressure  of  55  Ibs.  per  square  foot  of  vertical  surface  to  be  applied  to  the 
structure.  The  surface  of  boats  exposed  to  the  wind  may  be  reckoned  as  a  rectangle 
4-92  feet  above  the  side  of  the  tank,  and  having  the  same  length  as  the  bridge. 

PAKT   II 

KEGULATIONS   OF   AUGUST   29,    1891,   AS   TO   TESTS   OF   METALLIC 
BEIDGES   (ABEIDGED)1 

Railway  Bridges. 

EACH  metallic  span  will  be  subjected  to  (a]  dead  load  test,  (6)  rolling  load  test.  These 
tests  will  be  made  by  test  trains  at  least  equal  in  weight  to  the  type  trains  previously 
defined  in  these  regulations.  For  tests  by  dead  load  the  test  train  will  be  placed 
successively  in  the  positions  producing  the  greatest  stresses  in  the  principal  members 
of  the  bridge. 

For  separate  span  bridges  the  test  train  will  be  placed  successively  on  each  span, 
so  as  to  cover  it  completely,  then  to  cover  only  one-halt  of  each  span. 

For  continuous  span  bridges  each  span  will  be  loaded  by  itself  as  just  described. 
Then  there  will  be  loaded  simultaneously  the  two  spans  contiguous  to  each  pier, 
exclusively  of  all  the  others. 

For  arched  bridges  the  whole  span  will  first  be  loaded,  then  each  half  alone,  and 
finally  the  middle  portion,  by  placing  there  the  two  locomotives  head  to  head. 

For  the  dead  load  tests  the  test  train  will  remain  in  each  of  those  positions  for  at  least 
half  an  hour. 

The  live  load  tests  will  be  two  in  number — viz.,  at  speeds  of  12-5  and  25  miles  per  hour. 
The  latter  test  may  be  postponed  till  the  track  has  somewhat  consolidated. 

For  double  line  bridges  with  both  tracks  on  one  platform,  the  tests  will  be  made 
on  each  track  separately  as  explained  above,  the  other  track  remaining  unoccupied  ;  then 
on  both  tracks  simultaneously.  For  the  live  load  tests  the  trains  will  travel  in  the  same 
direction. 

For  bridges  of  exceptional  type,  special  arrangements  will  be  made  for  the  test. 

Road  Bridges. 

Metallic  spans  will  be  subjected  to  tests  of  two  kindn — viz.,  (a]  dead  load,  (&)  live 
load. 

For  the  dead  load  test  the  surcharge  will  be  82  Ibs.  per  square  foot  of  the  platform, 
including  the  footpaths. 

For  live  loads  the  loads  will  be  arranged  as  far  as  possible  as  to  weight  and  spacing 
like  the  type  load  used  in  the  calculation.  They  ought  to  give  at  least  with  their  yokes 
a  minimum  load  of  82  Ibs.  per  square  foot,  taking  7'38  feet  as  the  width  occupied.  The 
number  of  files  of  vehicles  ought  to  be  equal  to  the  width  of  the  roadway  divided  by  7*38  ; 
but  in  the  event  of  it  being  difficult  to  assemble  the  full  number  of  vehicles,  the  surplus 
width  might  be  occupied  by  a  dead  weight  of  82  Ibs.  per  square  foot  distributed  on  each 
side  of  the  files. 

For  dead  load  tests  of  separate  spans  the  load  will  be  extended  from  one  extremity  to 

1  "  Kesistance  des  Materiaux  "  (Vol.  I.,  p.  595),  Bibliotheque  du  Conducteur  de  Travaux 
Publics  ;  publishers,  Duuod  et  Pinat,  Paris. 


112  APPENDIX 

the  other,  with  a  stop  of  half  an  hour  when  the  load  has  reached  half  span,  and  the  full 
load  shall  remain  on  the  bridge  for  half  an  hour. 

For  continuous  bridges  each  span  will  be  first  loaded  separately,  as  described  above ; 
then  the  two  spans  contiguous  to  each  pier  will  be  loaded  simultaneously,  exclusively  of 
the  others. 

For  arched  bridges,  each  span  will  be  loaded  over  the  whole  span ;  then  on  each  half, 
and  finally  on  the  middle  portion  only. 

The  live  load  test  will  be  carried  out  by  causing  the  files  of  vehicles  to  pass  at  a 
walking  pace  from  one  extremity  of  the  bridge  to  the  other. 

There  will  also  be  made  to  pass  over  the  bridge  a  vehicle  with  an  axle  load  of  10'8  tons. 

When  a  reduction  has  been  allowed  in  the  loads  used  in  calculation,  the  test  loads  will 
be  correspondingly  reduced. 

Loads  notably  greater  than  the  test  loads  will  only  be  allowed  to  pass  over  the  bridge 
by  special  authorisation. 

Bridges  Carrying  Canals. 

The  tests  of  canal  bridges  will  consist  in  the  measurement  of  deflections  after  filling 
to  a  depth  of  12  inches  over  normal  water-level. 

Measurement  of  Deflections. 

There  will  be  measured  at  the  time  of  the  test  the  maximum  deflection  at  the  centre 
of  each  span,  under  the  influence  first  of  the  dead  load  and  then  of  the  live  load  in 
movement. 

When  there  are  several  bridges  of  identical  construction  and  of  span  not  exceeding 
33  feet,  the  measurement  of  deflection  need  only  be  made  for  one  of  them. 

Immediately  after  the  test  of  each  bridge  the  metallic  part  shall  be  examined  in  all 
its  details. 

For  bridges  over  33  feet  span  two  permanent  bench  marks  will  be  fixed  clear  of  every 
part  of  the  structure.  The  levels  of  the  lowest  parts  of  the  girders  or  arches  at  the  centre 
and  also  at  the  extremities  of  each  span  and  of  the  supports  shall  be  recorded  relative  to 
these  bench  marks. 

The  detailed  reports  of  the  test  made  by  the  engineer  in  charge,  in  the  form  pre- 
scribed by  the  Administration,  shall  contain  a  description  of  these  bench  marks,  which 
will  enable  them  to  be  found  at  any  subsequent  time. 

PAKT   III 

IMPOSED  LOADS  AND  TESTS  STIPULATED  IN  THE  REGULATIONS1 
OF  FEBEUAEY  17,  1903,  FOE  METALLIC  STATION  BUILDINGS 
(ABEIDGED) 

THE  snow  load  used  in  calculating  stresses  is  to  be  taken  at  12'3  Ibs.  per  square  foot 
of  horizontal  surface,  and  the  wind  pressure  at  31  Ibs.  per  square  foot  normal  to  its 
direction,  which  is  assumed  to  be  at  an  angle  of  10  degrees  to  the  horizontal  downwards 
towards  the  earth. 

If  a°  is  the  angle  of  inclination  of  the  roof,  the  action  of  the  wind  might  be  replaced 
by  a  vertical  surcharge  equal  to  31  sin  2  (a  -f-  10)  Ibs.  per  square  foot  of  surface  covered, 
and  a  horizontal  thrust  having  the  same  value  31  sin  2  (a  -f  10)  Ibs.  per  square 
foot  of  surface  in  elevation. 

The  maximum  wind  might  occur  even  after  a  fall  of  snow,  but  in  that  case  the  weight 
of  snow  may  be  considered  as  6'2  Ibs.  per  square  foot  of  horizontal  surf  ace. 

After  erection  one  or  several  of  the  main  trusses  are  to  be  submitted,  as  far  as 
possible,  to  tests  intended  to  demonstrate  their  resistance  to  forces  analogous  to  those 
which  they  will  be  called  upon  to  support.  The  results  obtained  by  measurements 
during  the  tests  wjll  be  compared  with  those  furnished  by  the  calculations. 

For  works  constructed  or  contracted  for  by  the  concessionaires,  the  tests  are  to  be  made 
in  the  presence  of  the  engineer  charged  with  the  control  of  the  tests,  or  of  an  agent 
delegated  by  him.  Detailed  special  reports  of  the  tests  are  to  be  sent  to  the  Administration, 
which  reserves  the  right  to  make  any  modification  in  the  regulations  to  meet  exceptional 
cases. 

1  "  Resistance  des  Materiaux "  (Vol.  III.,  p.  506),  Bibliotheque  du  Conducteur  de  Travaux 
Publics  ;  publishers,  Dunod  et  Pinat,  Paris. 


BIBLIOGRAPHY 

BEITISH  AND  AMEEICAN  PUBLICATIONS. 

1905.  CONCRETE  STEEL.    W.  N.  TWELVETREES.    Whittaker  &  Co.     6s.  net. 

1906.  EEINFORCED  CONCRETE  ;  A  HANDBOOK.    F.  D.  WARREN.    Crosby  Lockwood  & 

Son.     10s.  Qd.  net. 
EEINFORCED  CONCRETE  CONSTRUCTION.      BUEL  AND  HILL.    Hill  Publishing  Co. 

21s.  net. 
EXPERIMENTAL    EESEARCHES    ON    EEINFORCED    CONCRETE.      A.   CONSIDERE. 

Translated  by  LEON.   S.   MOISSIEFF.      Hill    Publishing  Co.      2nd  Edition. 

8s.  Qd.  net. 

1907.  EEINFORCED  CONCRETE.    MARSH  AND  DUNN.     Constable  &  Co.    31s.  Qd.  net. 
THE  ELASTIC  ARCH.     BURTON  L.  LEFFLER.    Constable  &  Co.    4s.  net. 
EEINFORCED  CONCRETE  DESIGN  ;   A   GRAPHICAL  HANDBOOK  (containing  New 

York  Building  Code).      JOHN  HAWKSWORTH.     Crosby   Lockwood   &    Son. 

12s.  net. 

CONCRETE  STEEL  BUILDINGS.     W.  N.  TWELVETREES.    Whittaker  &  Co.    10s.  net. 
EEINFORCED  CONCRETE.     Lieut. -Col.  WINN.      The  Eoyal  Engineers'  Institute, 

Chatham.     2s.  Qd.  net. 

1908.  THEORY  AND  DESIGN  OF  EEINFORCED  CONCRETE  ARCHES.    ARVID  EEUTERDAHL. 

The  Myron  0.  Clark  Publishing  Co.     8s.  Qd.  net. 

EEINFORCED  CONCRETE  ;  A  MANUAL  OF  PRACTICE.  ERNEST  MCCULLOUGH. 
The  Myron  C.  Clark  Publishing  Co.  6*.  6^.  net. 

CONCRETE  SYSTEM.    FRANK  B.  GILB.RETH.    Hill  Publishing  Co.     20s.  net. 

ARCHITECTS'  AND  ENGINEERS'  HANDBOOK  OF  EEINFORCED  CONCRETE  CON- 
STRUCTION. L.  T.  MENSCH.  Hill  Publishing  Co.  8s.  Qd.  net. 

EEINFORCED  CONCRETE  DIAGRAMS  FOR  THE  CALCULATION  OF  BEAMS,  SLABS 
AND  COLUMNS.  G.  S.  COLEMAN.  Crosby  Lockwood  &  Son.  3s.  Qd.  net. 

CONCRETE  CONSTRUCTION  ;  METHODS  AND  COSTS.  GILLETTE  AND  HILL.  Myron 
C.  Clark  Co.  21s.  net. 

1909.  A  CONCISE  TREATISE  ON  EEINFORCED  CONCRETE.    C.  F.  MARSH.    Constable  & 

Co.     7s.  Qd.  net. 
CONCRETE     STEEL    CONSRUCTION.      EMILE    MORSCH.      Translated    by    E.    P. 

GOODRICH.     Hill  Publishing  Co.     21s.  net. 
PRINCIPLES  OF  EEINFORCED  CONCRETE  CONSTRUCTION.    TURNEAURE  MAURER. 

Chapman  and  Hall.     los.  net. 
ENGINEERS'  POCKET  BOOK  OF  EEINFORCED   CONCRETE.     E.  L.  HEIDENREICH. 

The  Myron  C.  Clark  Co.     12s.  Qd.  net 
THE  ELEMENTS  OF  EEINFORCED  CONCRETE  BUILDING.     G.  A.  T.  MIDDLETON. 

Francis  Griffiths.     4s.  net. 
INSPECTORS'  HANDBOOK  OF  EEINFORCED  CONCRETE.     W.  F.  BALLINGER.    Hill 

Publishing  Co.     4s.  net. 
CONCRETE  PLAIN  AND  EEINFORCED.    TRAUTWINE.    Chapman  and  Hall.    8s.  Qd. 

net. 

1910.  MANUAL    OF    EEINFORCED    CONCRETE.      2nd    Edition.       MARSH    AND    DUNN. 

Constable  &  Co.     7s.  Qd.  net. 
EXTRACTS  ON  EEINFORCED  CONCRETE  DESIGN.    TAYLOR  AND  THOMSON.   Chapman 

and  Hall.     8s.  Qd.  net. 
CONCRETE  AND  EEINFORCED  CONCRETE  CONSTRUCTION.    HOMER  A.  EEID.     The 

Myron  C.  Clark  Co.     21s.  net. 

EEINFORCED  CONCRETE.    WEBB  GIBSON,   Crosby  Lockwood  &  Son.     4s.  Qd.  net. 
EEINFORCED  CONCRETE  THEORY  AND  PRACTICE:    F.  EINGS.    Batsford.     7s.  Qd. 

net. 
R.c.  I 


114  BIBLIOGRAPHY 

REINFORCED  CONCRETE.     Captain  J.  G.  FLEMING,  R.E.      The  Royal  Engineers' 

Institute,  Chatham.     3s.  6d.  net. 
BRAYTON  STANDARDS  FOR  THE  UNIFORM   DESIGN   OF   REINFORCED   CONCRETE. 

Louis  F.  BRAYTON.     2nd  Edition.     Hill  Publishing  Co.     12s.  Qd.  net. 
DIAGRAMS  FOR  DESIGNING  REINFORCED  CONCRETE  STRUCTURES.    G.  F.  DODGE. 

Spon.     17s.  net. 
A  TECHNICAL  DICTIONARY  IN  Six   LANGUAGES    OF   REINFORCED  CONCRETE  IN 

SUB-  AND  SUPERSTRUCTURE.     Constable.     6s.  net. 
1911.    TREATISE   ON  CONCRETE,  PLAIN  AND   REINFORCED.     TAYLOR   AND    THOMSON. 

2nd  Edition.     Chapman  and  Hall.     21s.  net. 
REINFORCED    CONCRETE,   COMPRESSION    MEMBER   DIAGRAM.      C.    F.  MARSH. 

Constable  &  Co.     Unmounted,  3s.  6d.  net. 
LECTURES  ON  REINFORCED  CONCRETE.    WILLIAM  DUNN.    Hodder  and  Stoughton. 

7s.  Gd.  net. 
DIAGRAMS  FOR  SOLUTION  OF  T-BEAMS  IN  REINFORCED   CONCRETE.    WILLIAM 

DUNN.     Hodder  and  Stoughton.     5s.  net. 
REINFORCED  CONCRETE  IN  THEORY  AND  PRACTICE.     ADAMS  AND  MATTHEWS. 

Longmans,  Green  &  Co.     10s.  6d.  net. 
PLAIN  AND  REINFORCED  CONCRETE.    (Section  5,  American  Civil  Engineers'  Pocket 

Book.)     F.  E.  TURNEAURE.     Wiley  &  Sons.     21s.  net. 
REINFORCED  CONCRETE  CONSTRUCTION.    Elementary  Course.     M.  T.  CANTELL. 

Spon.     4s.  6d.  net. 
R.I.B.A.  REPORT  OF  THE  JOINT  COMMITTEE  ON  REINFORCED  CONCRETE.    Second 

Edition.     Is.  net. 
REINFORCED    CONCRETE    CONSTRUCTION.      E.    ANDREWS.      Scott    Greenwood. 

3s.  net. 
REINFORCED  CONCRETE  BEAMS  AND  COLUMNS.    W.  N.  TWELVETREES.    Whittaker. 

6s.  net. 
REINFORCED    CONCRETE    DESIGN    SIMPLIFIED.      JOHN    C.    GAMMON.      Crosby 

Lockwood.     10s.  6d.  net. 

GRAPHICAL  REINFORCED  CONCRETE  DESIGN.    J.  A.  DAVENPORT.     Spon.     5s.  net. 
REINFORCED    CONCRETE,   MECHANICS    AND    ELEMENTARY    DESIGN.      JOHN    P. 

BROOKS.     Hill  Publishing  Co.     8s.  6d.  net. 
1912.     REINFORCED  CONCRETE  DESIGN.     FABER  AND  BOWIE.     Arnold.     12s.  Qd.  net. 

Tn  addition  to  the  a^ove  the  Proceedings  of  the  Concrete  Institute  and  the  Proceedings 
of  the  Institution  of  Civil  Engineers  contain  information  regarding  Reinforced  Concrete. 
The  Preliminary  and  Interim  Report  of  the  Committee  of  the  Institution  of  Civil 
Engineers  on  Reinforced  Concrete  contains  a  list  of  Papers  and  Abstracts  referring  to 
Reinforced  Concrete  in  recent  volumes  of  the  Proceedings. 

SOME  FRENCH  PUBLICATIONS. 

LE  BETON  ARME  ET  SES  APPLICATIONS.     PAUL  CHRISTOPHE.     Beranger,  Paris. 

32*. 
RESISTANCE  DU  BE"TON  ET  DU  CIMENT  ARME.      TEDESCO  ET  MAUREL.    Beranger, 

Paris.     20s. 
LE  BETON  FRETTE  ET   SES  APPLICATIONS.     A.  CONSIDERS.     Dunod  et  Pinat, 

Paris.     2s. 
LA  CONSTRUCTION  EN  CIMENT  ARME.      BERGER  ET   GUILLERME.     Dunod  et 

Pinat,  Paris.     40s. 
COMMISSION  DU  CIMENT  ARM£  :  EXPERIENCES,  RAPPORTS,  ETC.     Dunod  et  Pinat, 

Paris.     22s. 
BETON  ARM£.     VOL.  I.  PROCEDES  GENERAUX  DE  CONSTRUCTION  ET  CALCUL  DES 

OUTRAGES.     VOL.  II.  APPLICATIONS  DU  BETON  ARME.    LIEUT.-COL.  M.  G. 

ESPITALLIER.     iWe  Speciale  des  Travaux  Publics. 

SOME   GERMAN  PUBLICATIONS. 

HANDBUCH    FUR    EISENBETONBAU.      Edited   by    DR.    ING.    F.    v.   EMPERGER. 
Wilhelm  Ernst  u.  Sohn,  Berlin. 

DlE    ElSENBETONLITERATUR    BIS    ENDE    1911.       Von    INGENIEUR    R.    HOFFMANN. 

Wilhelm  Ernst  u.  Sohn,  Berlin. 


BIBLIOGRAPHY  115 

DER     ElSENBETONBAU     EIN     LEITFADEN    FUR    SCIIULE    UND     PRAXIS.       Von     C. 

KERSTEN.     Wilhelm  Ernst  u.  Sohn,  Berlin. 
BRUCKEN  IN  EISENBETON.      TEIL  I.  FLATTEN  u.  BALKENBRUCKEN.      TEIL  II. 

BOGENBRUCKEN.     C.  KERSTEN.     Wilhelm  Ernst  u.  Sohn. 
DIE  THEORIE  DES  EISENBETONBAUES.     PROF.  M.  FOERSTER,  Dresden.    Julius 

Springer,  Berlin. 
TABELLEN   FUR   DIE    BERECHNUNG  VON   EISENBETONKONSTRUKTIONEN.      Von 

INGENIEUR  G.  FUNKE.    Julius  Springer,  Berlin. 

EISENBETONBRUCKEN.     DR.  ING.  F.  KoGLER,  Dresden.     Julius  Springer,  Berlin. 
There  are  also  the  publications  of  the  Deutscher  Ausschuss  f  iir  Eisenbeton.    Published 
by  Wilhelm  Ernst  u.  Sohn. 

PERIODICALS. 

In  addition  to  the  articles  on  Reinforced  Concrete  in  the  general  engineering 
periodicals,  the  following  are  wholly  or  largely  devoted  to  that  subject  : — 

CONCRETE  AND  CONSTRUCTIONAL  ENGINEERING.  Published  at  the  North  British 
and  Mercantile  Building,  Waterloo  Place,  London.  Monthly,  Is.  Per 
annum,  12s.  6rf. 

FERRO-CONCRETE.      A    Monthly    Review    of    Hennebique    Construction.      The 
St.  Bride's  Press,  Ltd.,   24,   St.  Bride's  Lane,  E.C.     Monthly,  6d.     6s.  per 
annum. 
CEMENT  AGE  AND   CONCRETE  ENGINEERING.      Cement   Age  Co.,   New  York. 

$1.50  per  annum. 

CEMENT  ERA.     Chicago.     Monthly.     $1.00  per  annum. 

In  addition,  Bulletins  are  issued  by  the  United  States  Government  Departments  and 
the  American  Universities  from  time  to  time.  Particulars  of  these  can  be  had  from  the 
Technical  Literature  Company,  90,  West  Street,  New  York,  or  Messrs.  Constable  &  Co., 
10,  Orange  Street,  Leicester  Square,  London. 

The  principal  French  and  German  periodicals  are  : — 

LE  BETON  ARME,   CIMENT,   NOUVELLES  ANNALES  DE  LA  CONSTRUCTION,   and 
REVUE    DES    MATERIAUX    DE    CONSTRUCTION    ET   DE    TRAVAUX   PUBLICS, 
published  in  Paris. 
BETON  u.  EISEN,   ZEMENT  u.   BETON,  and  ARMIERTER  BETON,   published  in 

Berlin. 

Particulars  of  which  can  be  obtained  from  any  of  the  French  or  German  publishers 
mentioned  above. 


INDEX 


ADHESION  of  the  concrete  to  the  reinforcements, 

16,  79,  87 

values  of  stresses  on,  100 
ARCH  ribs,  stresses  in,  12 

BEAMS,  continuous,  stresses  in,  12 

experiments  on  bending  of,  30 
notes  on  bending  experiments,  95 
BENDING,  calculation  of  stress  due  to,  13 
combined  with  thrust,  14 
effects  of  transverse  reinforcements 

in,  101 
BRIDGES,  live  loads  on,  109 

tests  of,  111 

BUCKLING  of  compression  members,  17 
BUILDINGS,  loads  and  tests,  112 

CALCULATIONS  of  resistance,  instructions  re- 
garding, 2 
simplification  of,  81 
CANAL  bridges,  110,  111 
CEMENT,  properties  of  cement  used  in  tests, 

40 
CENTRE  of    gravity    in    reinforced    members, 

10 
COLUMNS,  strength  of  concrete  at  base  and  top, 

59,  74 

safe  loads  on  highly  spiralled,  84 
actual  conditions  of  in  practice,  85 
experiments  on  eccentric  loading  of 

49,  85 
long,  83 

limits  of  working  stress  in,  84 
estimation  of  stability  of,  17 
exposed  to  lateral  pressure,  18 
tests  of,  48 
tests  on  axially  loaded  columns,  50, 

51 

hollow,  tests  of,  64 
Stuttgart,  experiments  on,  20 
variously  reinforced  tests  of,  57 
COLUMN  reinforcement,  most  efficient  percent- 
ages, 84 
COMPRESSION,  calculation     of     simple     com- 

pressive  resistance,  9 
with    bending,    calculation    of 
resistance,  9,  85 


COMPRESSION  reinforcements,    comparison    of 

longitudinals  and  spirals,  82 
COMPRESSIVE   STRESSES   allowed    by   French 

regulations,  7 
allowed   by   Foreign 

regulations,  7 

CONCRETE,  reinforced  and  without  reinforce- 
ment, weight  of,  23,  57 
volume  of,  from  given  mixture, 

68 

CONSIDERE,  notes  by,  91 
CONTINUOUS  beams,  stresses  in,  12 
CONTRACTION,  during  setting  of  concrete,  22 

measurement  of,  22 
CRACKS,  influence  on  resistance  of  compression 

areas,  100 
CRUSHING,  resistance  of  concrete  to,  69 

increase     due     to     rein- 
forcements, 70,  73 

DEFLECTION  of  beams,  measurement  of,  31 

curve  of,  40,  41 

of  slab,       load-deflection       dia- 
grams, 42 

characteristics  of,   46 
DEFORMATION  of  reinforced  concrete,  93 

in  beams,  98 

of  plane  sections  during  bend- 
ing, 78,  96 

laws  of,  applied  to  bending,  79 
estimation  of,  91 

ELASTICITY,  modulus  of  concrete  without  rein- 
forcement, 18,  22 
modulus  of  reinforced  concrete, 

77 
ratio  of  the  moduli  for  concrete 

and  steel,  8 

modulus  of,  for  steel,  18,  26 
ELASTIC  effect  of  longitudinal  reinforcements, 

77 
ELONGATION  of  reinforcements,  curve  of,  41 

reinforced    concrete    without 

cracking,  93 

EMPIRICAL  formulae,  89 
EULER'S  formula  for  long  columns,  18 
EXPERIMENTS  on  actual  works,  80 


118 


INDEX 


FACTOR  of  safety,  6,  20,  81 
FINAL  state  of  stress  in  a  member  after  un- 
loading, 95 

GRAVITY,  centre  of  in  reinforced  members,   10 

HEAT,  variations  of  volume  of  concrete  due  to, 
68 

INERTIA,    determination  of  moment  of,  10 

LOADS  imposed  on  structures,  1,  109 
LOADING  and  unloading,  effects  of,  94 
LONGITUDINALLY  reinforced  prisms,  compres- 
sion tests  of,  57 

LONGITUDINAL  reinforcements  compared  with 
spirals,  82 

"  m,"  values  of,  9,  19,  71 

effect  of  exaggerating  value  in  members 

subject  to  bending,  86 
"  m',"  values  of,  8,  71 

MODULUS  of  elasticity  of   non-reinforced   con- 
crete, 18,  22 
of  reinforced  concrete, 

77 

MOMENT  of  inertia  of  section  of  reinforced 
members,  10 

NAVIER'S  hypothesis,  graphical  verifications  of, 

39,47 
NEUTRAL  axis,  position  of,  13,  96 

comparison  of  actual  and   cal- 
culated positions,  97 

PERCENTAGE  of  reinforcement,  influence  of  on 
stresses  due  to  setting,  23,  96,  105 

PITCH  of  spirals  in  spiral  reinforcement,  8,  21, 
71 

PRISMS  without  reinforcement,  compression 
tests  of,  54-55 

RAILWAY  bridges,  loads  on  French  bridges,  109 
RANKINE'S  formula  for  long  columns,  17 
REACTIONS,  reciprocal  after  unloading,  95 
RECTANGULAR  beam,  calculation  of  stresses  in, 

13 
REINFORCEMENTS,  slipping  of,  16,  27,  99 

effect     of     pro- 
jecting over   points   of 
support,  87 
modulus  of  elasticity  of,  18, 

26 

transverse  in  members  sub- 
ject to  bending,  88 
REPETITION  of  loading,  effects  of,  94 
RESISTANCE  of  columns,  variations  through- 
out the  length,  74 

RIBBED  slabs,  experiments  on,  46,  103 
ROAD  bridges,  loads  on,  110 


SAFETY,  factor  of,  6,  20,  81 
SETTING  of  concrete,  stresses  due  to,  23,  93,  96, 
105 

cement,  variations  in  volume  due 

to,  68 

SHEAR  resistance,  estimation  of,  16 
SHEAR — resistance  of  reinforcements  to,   80, 

102 

SHEAR  reinforcements,  tests  of,  25 
SHEAR  strains  in  concrete  of  beam,    curve    of, 

41 

SHOCKS,  effect  of,  on  the  resistance  of  rein- 
forced concrete,  107 

SLABS,  remarks  on  the  calculation  of,  15 
with  concentrated  loads,  15 
width  of  acting  with  rib,  15,  104 
supported  along  four  sides,  16 
transverse  reinforcements  in,  89 
experiments  on  bending  of,  42 
graphical  representation  of  strains  in, 

47 

SLEEPER,  experiments  with  a  reinforced  con- 
crete sleeper,  107 
SLIPPING  of  reinforcements,  resistance  to,   16, 

99 

experiments  on,  27 

SLIPPING  of  the  concrete  on  itself,  16 
SNOW  loads  on  roofs,  112 
SPIRAL  reinforcements,  analysis  of  effect  of,  82 
SPIRALLED     column,    increase     of    allowable 

stress  due  to  spiralling,  7 

SPIRALLED  prisms,  compression  tests  of,  55,  56 
SPIRALLING,  instructions  regarding,  1 
SPIRALS,  intertwining,  experiments  on,  66 

multiple  concentric,  experiments  on, 

64 

pitch  of,  8,  21,  71,  77 
STEEL,  modulus  of  elasticity  of.  18,  26 
STIRRUPS,  effects  of  in  bending,  101,  102 
STRAINS  in  slab,  graphical  representation  of, 

47 

STRESS,  limits  of,  1 

STRESSES  and  deformations  of  reinforced  con- 
crete, 81 

STRESSES,  initial  due  to  setting,  23,  93,  96,  105 
effects  of  high  compressive  stresses 

in  concrete,  75 
allowable  in  French  bridges  (steel), 

109 
SYMBOLS,  5 

T  slab,  calculation  of  stresses  in,  13 
TENSION  tests  on  reinforced  concrete,  23,  66 

analysis  of  results  of,  91 
resistance  and  deformation  of  con- 
crete  without   reinforcement   due 
to,  69 


INDEX 


119 


TENSION,  effects  of  on  the  resistance  and  elas- 
ticity of  concrete  to  compression, 
94 
in  members  subject  to  bending,  effect 

of  neglecting  in  calculations,  86 
TESTS  of  structures,  3,  90,  111 
TORSION  tests,  27 
TRANSVERSE  reinforcements,  notes  on  effects 

of,  101 

increase  of  com- 
pressive  stress 
due  to,  7,  71 

TRANSVERSE     reinforcements,     resistance     to 
slipping  of  concrete,  17 


TRANSVERSE  reinforcements,  comparison  with 
longitudinal  reinforcements,  82 

VOLUME  of  concrete  resulting  from  given 
mixture,  68 

WATER,  influence  of  proportion  of  water  used 
in  gauging,  22,  74,  106 

WEIGHT  of  concrete  with  and  without  rein- 
forcement, 23,  57 

WIND  pressure,  110,  112 

WORKS,  instructions  regarding  execution 
of,  2 


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How  to  Use  Water  Power i2mo,  *i  oo 

Child,  C.  D.    Electric  Arc 8vo,    *(In  Press.) 

Child,  C.  T.     The  How  and  Why  of  Electricity i2mo,  i  oo 

Christie,  W.  W.     Boiler- waters,  Scale,  Corrosion,  Foaming 8vo,  *3  oo 

Chimney  Design  and  Theory 8vo,  *3  oo 

Furnace  Draft.     (Science  Series  No.  123.) i6mo,  o  50 

Water:  Its  Purification  for  Use  in  the  Industries 8vo,  (In  Press.) 

Church's  Laboratory  Guide.     Rewritten  by  Edward  Kinch 8vo,  *2  50 

Clapperton,  G.     Practical  Papermaking 8vo,  2  50 


D.  VAN   NOSTRAND  COMPANY'S   SHORT  TITLE   CATALOG       7 

Clark,  A.  G.     Motor  Car  Engineering. 

Vol.  I.     Construction *3  oo 

Vol.  H.    Design (In  Press.} 

Clark,  C.  H.     Marine  Gas  Engines i2mo,  *i  50 

Clark,  D.  K.     Rules,  Tables  and  Data  for  Mechanical  Engineers 8vo,  5  oo 

Fuel:  Its  Combustion  and  Economy i2mo,  i  50 

The  Mechanical  Engineer's  Pocketbook i6mo,  2  oo 

Tramways:  Their  Construction  and  Working 8vo,  5  oo 

Clark,  J.  M.     New  System  of  Laying  Out  Railway  Turnouts i2mo,  i  oo 

Clausen-Thue,  W.     ABC  Telegraphic  Code.     Fourth  Edition i2mo,  *s  oo 

Fifth  Edition 8vo,  *7  oo 

The  A  i  Telegraphic  Code 8vo,  *7  50 

Cleemann,  T.  M.     The  Railroad  Engineer's  Practice I2mo,  *i  50 

Clerk,  D.,  and  Idell,  F.  E.     Theory  of  the  Gas  Engine.     (Science  Series 

No.  62.) i6mo,  o  50 

Clevenger,  S.  R.     Treatise    on   the   Method   of   Government   Surveying. 

i6mo,  morocco 2  ^50 

Clouth,  F.     Rubber,  Gutta-Percha,  and  Balata 8vo,  *5^oo 

Cochran,  J.    Treatise  on  Cement  Specifications 8vo,  (In  Press.). .  3\J 

Coffin,  J.  H.  C.     Navigation  and  Nautical  Astronomy i2mo,  *3  50 

Colburn,  Z.,  and  Thurston,  R.  H.     Steam  Boiler  Explosions.     (Science 

Series  No.  2.) i6mo,  o  50 

Cole,  R.  S.    Treatise  on  Photographic  Optics i2mo,  i  50 

Coles-Finch,  W.     Water,  Its  Origin  and  Use 8vo,  *s  oo 

Collins,  J.  E.     Useful  Alloys  and  Memoranda  for  Goldsmiths,  Jewelers. 

16010 o  50 

Constantine,  E.     Marine  Engineers,  Their  Qualifications  and  Duties.    8vo,  *2  oo 

Coombs,  H.  A.     Gear  Teeth.     (Science  Series  No.  120.) i6mo,  o  50 

Cooper,  W.  R.     Primary  Batteries 8vo,  *4  oo 

"  The  Electrician  "  Primers . . . ' 8vo,  *5  oo 

Part  I *i  50 

Part  II *2  50 

Part  III *2  oo 

Copperthwaite,  W.  C.     Tunnel  Shields 4to,  *g  oo 

Corey,  H.  T.     Water  Supply  Engineering 8vo  (In  Press.) 

Corfield,  W.  H.     Dwelling  Houses.     (Science  Series  No.  50.) i6mo,  o  50 

Water  and  Water-Supply.     (Science  Series  No.  17.) i6mo,  o  50 

Cornwall,  H.  B.     Manual  of  Blow-pipe  Analysis 8vo,  *2  50 

Courtney,  C.  F.     Masonry  Dams 8vo,  3  50 

Cowell,  W.  B.     Pure  Air,  Ozone,  and  Water i2mo,  *2  oo 

Craig,  T.     Motion  of  a  Solid  in  a  Fuel.     (Science  Series  No.  49.) ....  i6mo,  o  50 

-  Wave  and  Vortex  Motion.     (Science  Series  No.  43.) i6mo,  o  50 

Cramp,  W.     Continuous  Current  Machine  Design 8vo,  *2  50 

Crocker,  F.  B.     Electric  Lighting.     Two  Volumes.     8vo. 

Vol.    I.     The  Generating  Plant 3  oo 

Vol.  II.     Distributing  Systems  and  Lamps 3  oo 

Crocker,  F.  B.,  and  Arendt,  M.     Electric  Motors 8vo,  *2  50 

Crocker,  F.  B.,  and  Wheeler,  S.  S.     The  Management  of  Electrical  Ma- 
chinery  i2ino,  *i  oo 

Cross,  C.  F.,  Bevan,  E.  J.,  and  Sindall,  R.  W.     Wood  Pulp  and  Its  Applica- 
tions.    (Westminster  Series.) 8vo,  *2  oo 


8       D.  VAN   NOSTRAND   COMPANY'S  SHORT  TITLE  CATALOG 

Crosskey,  L.  R.     Elementary  Perspective 8vo,  i  oo 

Crosskey,  L.  R.,  and  Thaw,  J.    Advanced  Perspective 8vo,  i  50 

Culley,  J.  L.      Theory  of  Arches.     (Science  Series  No.  87.) i6mo,  o  50 

Davenport,  C.     The  Book.     (Westminster  Series.) 8vo,  *2  oo 

Davies,  D.  C.     Metalliferous  Minerals  and  Mining 8vo,  5  oo 

Earthy  Minerals  and  Mining 8vo,  5  oo 

Davies,  E.  H.     Machinery  for  Metalliferous  Mines 8vo,  8  oo 

Davies,  F.  H.     Electric  Power  and  Traction 8vo,  *2  oo 

Dawson,  P.     Electric  Traction  on  Railways 8vo,  *p  oo 

Day,  C.     The  Indicator  and  Its  Diagrams i2mo,  *2  oo 

Deerr,  N.     Sugar  and  the  Sugar  Cane 8vo,  *3  oo 

Deite,  C.     Manual  of  Soapmaking.     Trans,  by  S.  T.  King 4to,  *5  oo 

De  la  Coux,  H.     The  Industrial  Uses  of  Water.     Trans,  by  A.  Morris. 

8vo,  *4  50 

Del  Mar,  W.  A.     Electric  Power  Conductors 8vo,  *2  oo 

Denny,  G.  A.     Deep-level  Mines  of  the  Rand 4to,  *io  oo 

Diamond  Drilling  for  Gold *5  oo 

De  Roos,  J.  D.  C.     Linkages.     (Science  Series  No.  47.) i6mo,  o  50 

Derr,  W.  L.     Block  Signal  Operation Oblong  i2mo,  *i  50 

Maintenance-of-Way  Engineering (In  Preparation.) 

Desaint,  A.     Three  Hundred  Shades  and  How  to  Mix  Them 8vo,  *io  oo 

De  Varona,  A,     Sewer  Gases.     (Science  Series  No.  55.).. i6mo,  o  50 

Devey,  R.  G.     Mill  and  Factory  Wiring.     (Installation  Manuals  Series.) 

i2mo,  *i  oo 

Dibdin,  W.  J.     Public  Lighting  by  Gas  and  Electricity 8vo,  *8  oo 

Purification  of  Sewage  and  Water 8vo,  6  50 

Dichmann,  Carl.    Basic  Open-Hearth  Steel  Process i2mo,  *3  50 

Dieterich,  K.     Analysis  of  Resins,  Balsams,  and  Gum  Resins. 8vo,  *3  oo 

Dinger,  Lieut.  H.  C.     Care  and  Operation  of  Naval  Machinery i2mo,  *2  oo 

Dixon,  D.  B.     Machinist's  and  Steam  Engineer's  Practical  Calculator. 

i6mo,  morocco,  i  25 

Doble,  W.  A.     Power  Plant  Construction  on  the  Pacific  Coast  (In  Press.) 
Dodd,  G.     Dictionary    of   Manufactures,    Mining,    Machinery,    and    the 

Industrial  Arts i2mo,  i  50 

Dorr,  B.  F.     The  Surveyor's  Guide  and  Pocket  Table-book. 

i6mo,  morocco,  2  oo 

Down,  P.  B.     Handy  Copper  Wire  Table i6mo,  *i  oo 

Draper,  C.  H.     Elementary  Text-book  of  Light,  Heat  and  Sound. . .  i2mo,  i  oo 

Heat  and  the  Principles  of  Thermo-dynamics i2mo,  i  50 

Duckwall,  E.  W.     Canning  and  Preserving  of  Food  Products 8vo,  *5  oo 

Dumesny,'  P.,  and  Noyer,  J.     Wood  Products,  Distillates,  and  Extracts. 

8vo,  *4  50 
Duncan,  W.  G.,  and  Penman,  D.     The  Electrical  Equipment  of  Collieries. 

8vo,  *4  oo 
Dunstan,TA.  E.,  and  Thole,  F.  B.  T.    Textbook  of  Practical  Chemistry. 

i2mo,  *i  40 

Duthie,  A.  L.     Decorative  Glass  Processes.     (Westminster  Series.).  .8vo,  *2  oo 

Dwight,  H.  B.    Transmission  Line  Formulas 8vo,   (In  Press.) 

Dyson,  S.  S.     Practical  Testing  of  Raw  Materials 8vo,  *5  oo 

Dyson,  S.  S.,  and  Clarkson,  S.  S.     Chemical  Works 8vo,  *7  5<> 


D.   VAN   NOSTRAND   COMPANY'S   SHORT  TITLE  CATALOG        9 

Eccles,  R.  G.,  and  Duckwall,  E.  W.     Food  Preservatives 8vo,  paper  o  50 

Eddy,  H.  T.     Researches  in  Graphical  Statics 8vo,  i  50 

Maximum  Stresses  under  Concentrated  Loads 8vo,  i  50 

Edgcumbe,  K.     Industrial  Electrical  Measuring  Instruments 8vo,  *2  50 

Eissler,  M.     The  Metallurgy  of  Gold 8vo  7  50 

The  Hydrometallurgy  of  Copper 8vo,  *4  50 

The  Metallurgy  of  Silver 8vo,  4  oo 

The  Metallurgy  of  Argentiferous  Lead 8vo,  5  oo 

Cyanide  Process  for  the  Extraction  of  Gold 8vo,  3  oo 

A  Handbook  on  Modern  Explosives 8vo,  5  oo 

Ekin,  T.  C.     Water  Pipe  and  Sewage  Discharge  Diagrams folio,  *3  oo 

Eliot,  C.  W.,  and  Storer,  F.  H.     Compendious  Manual  of  Qualitative 

Chemical  Analysis i2mo,  *i  25 

Elliot,  Major  G.  H.     European  Light-house  Systems 8vo,  5  oo 

Ennis,  Wm.  D.     Linseed  Oil  and  Other  Seed  Oils 8vo,  *4  oo 

Applied  Thermodynamics 8vo  *4  50 

Flying  Machines  To-day I2mo,  *i  50 

Vapors  for  Heat  Engines i2mo,  *i  oo 

Erfurt,  J.     Dyeing  of  Paper  Pulp.     Trans,  by  J.  Hubner 8vo,  *7  50 

Erskine-Murray,  J.     A  Handbook  of  Wireless  Telegraphy 8vo,  *3  50 

Evans,  C.  A.     Macadamized  Roads (In  Press.) 

Ewing,  A.  J.     Magnetic  Induction  in  Iron 8vo,  *4  oo 

Fairie,  J.     Notes  on  Lead  Ores i2mo,  *i  oo 

Notes  on  Pottery  Clays i2mo,  *i  50 

Fairley,  W.,  and  Andre,  Geo.  J.     Ventilation  of  Coal  Mines.     (Science 

Series  No.  58.) i6mo,  o  50 

Fairweather,  W.  C.     Foreign  and  Colonial  Patent  Laws 8vo,  *3  oo 

Fanning,  J.  T.     Hydraulic  and  Water-supply  Engineering 8vo,  *5  oo 

Fauth,  P.      The  Moon  in  Modern   Astronomy.     Trans,  by  J.  McCabe. 

8vo,  *2  oo 

Fay,  I.  W.     The  Coal-tar  Colors 8vo,  *4  oo 

Fernbach,  R.  L.     Glue  and  Gelatine 8vo,  *3  oo 

Chemical  Aspects  of  Silk  Manufacture I2mo,  *i  oo 

Fischer,  E.     The  Preparation  of  Organic  Compounds.     Trans,  by  R.  V. 

Stanford i2mo,  *i  25 

Fish,  J.  C.  L.     Lettering  of  Working  Drawings Oblong  8vo,  i  oo 

Fisher,  H.  K.  C.,  and  Darby,  W.  C.     Submarine  Cable  Testing 8vo,  *3  50 

Fiske,  Lieut.  B.  A.     Electricity  in  Theory  and  Practice 8vo,  2  50 

Fleischmann,  W.    The  Book  of  the  Dairy.  Trans,  by  C.  M.  Aikman.   8vo,  4  oo 
Fleming,  J.  A.     The  Alternate-current  Transformer.     Two  Volumes'.    8vo. 

Vol.    I.     The  Induction  of  Electric  Currents *5  oo 

Vol.  II.     The  Utilization  of  Induced  Currents *5  oo 

Propagation  of  Electric  Currents 8vo,  *3  oo 

Centenary  of  the  Electrical  Current 8vo,  *o  50 

—  Electric  Lamps  and  Electric  Lighting 8vo,  *3  oo 

Electrical  Laboratory  Notes  and  Forms 4to,  *5  oo 

—  A  Handbook  for  the  Electrical  Laboratory  and  Testing  Room.     Two 

Volumes 8vo,  each,  *5  oo 

Fluery,  H.     The  Calculus  Without  Limits  or  Infinitesimals.     Trans,  by 
C.  0.  Mailloux. .  (In  Press.) 


10     D.   VAN  NOSTRAND  COMPANY'S  SHORT  TITLE   CATALOG 

tiynn,  P.  J.     Flow  of  Water.     (Science  Series  No.  84.) i6mo,  o  50 

Hydraulic  Tables.     (Science  Series  No.  66.) i6mo,  o  50 

Foley,  N,     British  and  American  Customary  and  Metric  Measures ..  folio,  *3  oo 
Foster,  H.  A.     Electrical  Engineers'  Pocket-book.     (Sixth  Edition.) 

i2mo,  leather,  5  oo 

Engineering  Valuation  of  Public  Utilities  and  Factories 8vo,  *3  oo 

Foster,  Gen.  J.  G.     Submarine  Blasting  in  Boston  (Mass.)  Harbor. .  .  .  4to,  3  50 

Fowle,  F.  F.     Overhead  Transmission  Line  Crossings i2mo,  *i  50 

The  Solution  of  Alternating  Current  Problems 8vo  (In  Press.) 

Fox,  W.  G.     Transition  Curves.     (Science  Series  No.  no.).. ......  i6mo,  o  50 

Fox,  W.,  and  Thomas,  C.  W.     Practical  Course  in  Mechanical  Draw- 
ing  i2mo,  i  25 

Foye,  J.  C.     Chemical  Problems.     (Science  Series  No.  69.) i6mo,  o  50 

Handbook  of  Mineralogy.     (Science  Series  No.  86.) i6mo,  o  50 

Francis,  J.  B.     Lowell  Hydraulic  Experiments 4to,  15  oo 

Freudemacher,    P.    W.     Electrical    Mining    Installations.     (Installation 

Manuals  Series  ) i2mo,  *i  oo 

Frith,  J.    Alternating  Current  Design 8vo,  *2  oo 

Fritsch,  J.     Manufacture  of  Chemical  Manures.    Trans,  by  D.  Grant. 

8vo,  *4  oo 

Frye,  A.  I.     Civil  Engineers'  Pocket-book i2mo,  leather, 

Fuller,  G.  W.      Investigations  into  the  Purification  of  the   Ohio  River. 

4to.  *io  oo 

Furnell,  J.     Paints,  Colors,  Oils,  and  Varnishes 8vo,  *i  oo 

Gairdner,  J.  W.  I.    Earthwork 8vo,   (In  Press.) 

Gant,  L.  W.     Elements  of  Electric  Traction 8vo,  *2  50 

Garforth,  W.  E.     Rules  for  Recovering  Coal  Mines  after  Explosions  and 

Fires i2mo,  leather,  i  50 

Gaudard,  J.     Foundations.     (Science  Series  No.  34.) i6mo,  o  50 

Gear,  H.  B.,  and  Williams,  P.  F.     Electric  Central  Station  Distribution 

Systems 8vo,  *3  oo 

Geerligs,  H.  C.  P.     Cane  Sugar  and  Its  Manufacture 8v6,  *s  oo 

Geikie,  J.     Structural  and  Field  Geology 8vo,  *4  oo 

Gerber,  N.   Analysis  of  Milk,  Condensed  Milk,  and  Infants' Milk-Food.    8vo,  i  25 
Gerhard,  W.  P.     Sanitation,  Watersupply  and  Sewage  Disposal  of  Country 

Houses i2mo,  *2  oo 

Gas  Lighting.     (Science  Series  No.  in.) i6mo,  o  50 

Household  Wastes.     (Science  Series  No.  97.) i6mo,  o  50 

• House  Drainage.     (Science  Series  No.  63.) i6mo,  o  50 

Sanitary  Drainage  of  Buildings.     (Science  Series  No.  93.) ....  i6mo,  o  50 

Gerhardi,  C.  W.  H.     Electricity  Meters 8vo,  *4  oo 

Geschwind,   L.     Manufacture   of   Alum   and   Sulphates.     Trans,   by   C. 

Salter 8vo,  *s  oo 

Gibbs,  W.  E.     Lighting  by  Acetylene i2mo,  *i  50 

Physics  of  Solids  and  Fluids.     (Carnegie  Technical  School's  Text- 
books.)   *i  50 

Gibson,  A.  H.     Hydraulics  and  Its  Application 8vo,  *5  oo 

Water  Hammer  in  Hydraulic  Pipe  Lines i2mo,  *2  oo 

Gilbreth,  F.  B.     Motion  Study i2mo,  *2  oo 

Primer  of  Scientific  Management i2mo,  *i  oo 


D.  VAN   NOSTRAND  COMPANY'S  SHORT  TITLE  CATALOG      11 

Gillmore,  Gen.  Q.  A.     Limes,  Hydraulic  Cements  ard  Mortars 8vo,  4  oo 

Roads,  Streets,  and  Pavements 121110,  2  oo 

Golding,  H.  A.     The  Theta-Phi  Diagram i2mo,  *i  25 

Goldschmidt,  R.     Alternating  Current  Commutator  Motor 8vo,  *3  oo 

Goodchild,  W.     Precious  Stones.     (Westminster  Series.) 8vo,  *2  oo 

Goodeve,  T.  M.     Textbook  on  the  Steam-engine i2mo,  2  oo 

Gore,  G.     Electrolytic  Separation  of  Metals 8vo,  *3  50 

Gould,  E.  S.     Arithmetic  of  the  Steam-engine i2mo,  i  oo 

Calculus.     (Science  Series  No.  112.) i6mo,  o  50 

High  Masonry  Dams.     (Science  Series  No.  22.) i6mo,  o  50 

Practical  Hydrostatics  and  Hydrostatic  Formulas.     (Science  Series 

No.  117.) i6mo,  o  50 

Grant,  J.     Brewing  and  Distilling.     (Westminster  Series.)  8vo  (In  Press.) 

Gratacap,  L.  P.    A  Popular  Guide  to  Minerals 8vo  (In  Press.) 

Gray,  J.     Electrical  Influence  Machines i2mo,  2  oo 

Marine   Boiler   Design i2mo,    (In  Press.) 

Greenhill,  G.    Dynamics  of  Mechanical  Flight 8vo,  (In  Press.) 

Greenwood,  E.     Classified  Guide  to  Technical  and  Commercial  Books.  8vo,  *3  oo 

Gregorius,  R.     Mineral  Waxes.     Trans,  by  C.  Salter I2mo,  *3  oo 

Griffiths,  A.  B.     A  Treatise  on  Manures i2mo,  3  oo 

—  Dental  Metallurgy 8vo,  *3  50 

Gross,  E.     Hops 8vo,  *4  50 

Grossman,  J.     Ammonia  and  Its  Compounds i2mo,  *i  25 

Groth,  L.  A.     Welding  and  Cutting  Metals  by  Gases  or  Electricity ....  8vo,  *3  oo 

Grover,  F.     Modern  Gas  and  Oil  Engines 8vo,  *2  oo 

Gruner,  A.     Power-loom  Weaving 8 vo,  *3  oo 

Gtlldner,  Hugo.     Internal  Combustion  Engines.     Trans,  by  H.  Diederichs. 

4to,  *io  oo 

Gunther,  C.  0.     Integration i2mo,  *r  25 

Gurden,  R.  L.     Traverse  Tables folio,  half  morocco,  *y  50 

Guy,  A.  E.     Experiments  on  the  Flexure  of  Beams 8vo,  *i  25 

Haeder,    H.      Handbook   on    the    Steam-engine.      Trans,  by  H.  H.  P. 

Powles i2mo,  3  oo 

Hainbach,  R.     Pottery  Decoration.     Trans,  by  C.  Slater i2mo,  *3  oo 

Haenig,  A.    Emery  and  Emery  Industry 8vo,  (In  Press.) 

Hale,  W.  J.     Calculations  of  General  Chemistry i2mo,  *i  oo 

Hall,  C.  H.     Chemistry  of  Paints  and  Paint  Vehicles i2mo,  *2  oo 

Hall,  R.  H.     Governors  and  Governing  Mechanism i2mo,  *2  oo 

Hall,  W.  S.     Elements  of  the  Differential  and  Integral  Calculus 8vo,  *2  25 

—  Descriptive  Geometry 8vo  volume  and  a  4to  atlas,  *3  50 

Haller,  G.  F.,  and  Cunningham,  E.  T.     The  Tesla  Coil I2mo,  *i  25 

Halsey,  F.  A.     Slide  Valve  Gears i2mo,  i  50 

-  The  Use  of  the  Slide  Rule.     (Science  Series  No.  114.) i6mo,  o  50 

-  Worm  and  Spiral  Gearing.     (Science  Series  No.  116.)        i6mo,  o  50 

Hamilton,  W.  G.     Useful  Information  for  Railway  Men i6mo, 

Hammer,  W.  J.     Radium  and  Other  Radio-active  Substances. .....  .8vo, 

Hancock,  H.     Textbook  of  Mechanics  and  Hydrostatics 8vo, 

Hardy,  E.     Elementary  Principles  of  Graphic  Statics I2mo, 

Harrison,  W.  B.     The  Mechanics'  Tool-book i2mo, 


oo 
oo 
50 
50 
50 


Hart,  J.  W.     External  Plumbing  Work 8vo,     *3  oo 


12     D.  VAN   NOSTRAND  COMPANY'S  SHORT  TITLE   CATALOG 

Hart,  J.  W.    Hints  to  Plumbers  on  Joint  Wiping 8vo,  *3  oo 

Principles  of  Hot  Water  Supply 8vo,  *3  oo 

Sanitary  Plumbing  and  Drainage 8vo,  *3  oo 

Haskins,  C.  H.     The  Galvanometer  and  Its  Uses i6mo,  i  50 

Hatt,  J.  A.  H.     The  Colorist square  i2mo,  *i  50 

Hausbrand,  E.     Drying  by  Means  of  Air  and  Steam.     Trans,  by  A.  C. 

Wright i2mo,  *2  oo 

Evaporating,  Condensing  and  Cooling  Apparatus.     Trans,  by  A.  C. 

Wright 8vo,  *5  oo 

Hausner,  A.     Manufacture  of  Preserved  Foods  and  Sweetmeats.     Trans. 

by  A.  Morris  and  H.  Robson 8vo,  *3  oo 

Hawke,  W.  H.     Premier  Cipher  Telegraphic  Code 4to,  *5  oo 

100,000  Words  Supplement  to  the  Premier  Code 4to,  *5  oo 

Hawkesworth,  J.     Graphical  Handbook  for  Reinforced  Concrete  Design. 

4to,  *2  50 

Hay,  A.     Alternating  Currents 8vo,  *2  50 

Electrical  Distributing  Networks  and  Distributing  Lines 8vo,  *3  50 

Continuous  Current  Engineering 8vo,  *2  50 

Heap,  Major  D.  P.     Electrical  Appliances 8vo,  2  oo 

Heaviside,  0.     Electromagnetic  Theory.     Two  Volumes .  8vo,  each,  *5  oo 

Heck,  R.  C.  H.    The  Steam  Engine  and  Turbine 8vo,  *5  oo 

Steam-Engine  and  Other  Steam  Motors.    Two  Volumes. 

Vol.    I.     Thermodynamics  and  the  Mechanics 8vo,  *3  50 

Vol.  II.     Form,  Construction,  and  Working 8vo,  *s  oo 

Notes  on  Elementary  Kinematics 8vo,  boards,  *i  oo 

Graphics  of  Machine  Forces 8vo,  boards,  *i  oo 

Hedges,  K.     Modern  Lightning  Conductors 8vo,  3  oo 

Heermann,  P.     Dyers' Materials.     Trans,  by  A.  C.  Wright i2mo,  *2  50 

Hellot,  Macquer  and  D'Apligny.     Art  of  Dyeing  Wool,  Silk  and  Cotton. 

8vo,  *2  oo 

Henrici,  0.     Skeleton  Structures 8vo,  i  50 

Bering,  D.  W.     Essentials  of  Physics  for  College  Students .8vo,  *i  60 

Hering-Shaw,  A.     Domestic  Sanitation  and  Plumbing.     Two  Vols. .  .  8vo,  *5  oo 

Elementary  Science 8vo,  *2  oo 

Herrmann,  G.     The  Graphical  Statics  of  Mechanism.     Trans,  by  A.  P. 

Smith i2mo,  2  oo 

Herzfeld,  J.     Testing  of  Yarns  and  Textile  Fabrics 8vo,  *3  50 

Hildebrandt,  A.     Airships,  Past  and  Present 8vo,  *3  50 

Hildenbrand,  B.  W.     Cable-Making.     (Science  Series  No.  32.) i6mo,  o  50 

Hilditch,  T.  P.     A  Concise  History  of  Chemistry i2mo,  *i  25 

Hill,  J.  W.     The  Purification  of  Public  Water  Supplies.      New  Edition. 

(In  Press.) 

—  Interpretation  of  Water  Analysis (In  Press.) 

Hiroi,  I.     Plate  Girder  Construction.     (Science  Series  No.  95.) i6mo,  050 

Statically-Indeterminate  Stresses i2mo,  *2  oo 

Hirshfeld,  C.  F.     Engineering  Thermodynamics.     (Science  Series  No.  45.) 

i6mo,  o  50 

Hobart,  H.  M.     Heavy  Electrical  Engineering 8vo,  *4  50 

Design  of  Static  Transformers i2mo,  *2  oo 

Electricity 8vo,  *2  oo 

Electric  Trains  .  .                                                     8vo,  *2  50 


D.   VAN   NOSTRAND   COMPANY'S  SHORT   TITLE  CATALOG      13 

Hobart,  H.  M.    Electric  Propulsion  of  Ships 8vo,  *2  oo 

Hobart,   J.   F.     Hard   Soldering,    Soft   Soldering   and    Brazing  12 mo, 

(In  Press.) 

Hobbs,  W.  R.  P.     The  Arithmetic  of  Electrical  Measurements i2mo,  o  50 

Hoff,  J.  N.     Paint  and  Varnish  Facts  and  Formulas i2ino,  *i  50 

Hoff,  Com.  W.  B.     The  Avoidance  of  Collisions  at  Sea.  .  .  i6mo,  morocco,  o  75 

Hole,  W.     The  Distribution  of  Gas 8vo,  *y  50 

Holley,  A.  L.     Railway  Practice folio,  12  oo 

Holmes,  A.  B.     The  Electric  Light  Popularly  Explained  ....  i2mo,  paper,  o  50 

Hopkins,  N.  M.     Experimental  Electrochemistry 8vo,  *3  oo 

Model  Engines  and  Small  Boats 12010,  i  25 

Hopkinson,  J.     Shoolbred,  J.  N.,  and  Day,  R.  E.     Dynamic  Electricity. 

(Science  Series  No.  71.) i6mo,  o  50 

Homer,  J.     Engineers'  Turning 8vo,  *3  50 

Metal  Turning I2mo,  i  50 

-  Toothed  Gearing i2mo,  2  25 

Houghton,  C.  E.     The  Elements  of  Mechanics  of  Materials i2mo,  *2  oo 

Houllevigue,  L.    The  Evolution  of  the  Sciences 8vo,  *2  oo 

Howe,  G.     Mathematics  for  the  Practical  Man i2mo,  *i  25 

Howorth,  J.     Repairing  and  Riveting  Glass,  China  and  Earthenware. 

8vo,  paper,  *o  50 

Hubbard,  E.     The  Utilization  of  Wood- waste 8vo,  *2  50 

Hu'bner,  J.    Bleaching  and  Dyeing  of  Vegetable  and  Fibrous  Materials 

(Outlines  of  Industrial  Chemistry) 8vo,  (In  Press.) 

Hudson,  O.  F.    Iron  and  Steel.     (Outlines  of  Industrial  Chemistry.) 

8vo,  (In  Press.) 

Humper,  W.     Calculation  of  Strains  in  Girders i2mo,  2  50 

Humphreys,  A.  C.     The  Business  Features  of  Engineering  Practice .  8vo,  *i  25 

Hunter,  A.     Bridge  Work 8vo,  (In  Press.) 

Hurst,  G.  H.     Handbook  of  the  Theory  of  Color 8vo,  *2  50 

—  Dictionary  of  Chemicals  and  Raw  Products 8vo,  *3  oo 

—  Lubricating  Oils,  Fats  and  Greases 8vo,  *4  oo 

—  Soaps 8vo,  *s  oo 

-  Textile  Soaps  and  Oils 8vo,  *2  50 

Hurst,  H.  E.,  and  Lattey,  R.  T.     Text-book  of  Physics 8vo,  *3  oo 

Hutchinson,  R.  W.,  Jr.     Long  Distance  Electric  Power  Transmission. 

i2mo,  *3  oo 

Hutchinson,  R.  W.,  Jr.,  and  Ihlseng,  M.  C.     Electricity  in  Mining.  .  i2mo, 

(In  Press) 

Hutchinson,  W.  B.     Patents  and  How  to  Make  Money  Out  of  Them.  i2mo,  i  25 

Hutton,  W.  S.     Steam-boiler  Construction 8vo,  6  oo 

—  Practical  Engineer's  Handbook 8vo,  7  oo 

-  The  Works'  Manager's  Handbook 8vo,  6  oo 

Hyde,  E.  W.     Skew  Arches.     (Science  Series  No.  15.) i6mo,  o  50 

Induction  Coils.     (Science  Series  No.  53.) i6mo,  o  50 

Ingle,  H.     Manual  of  Agricultural  Chemistry 8vo,  *3  oo 

Innes,  C.  H.     Problems  in  Machine  Design i2mo,  *2  oo 

Air  Compressors  and  Blowing  Engines i2mo,  *2  oo 

—  Centrifugal  Pumps i2mo,  *2  oo 

The  Fan i2mo,  *2  oo 


14     D.  VAN   NOSTRAND   COMPANY'S  SHORT  TITLE  CATALOG 

Isherwood,  B.  F.     Engineering  Precedents  for  Steam  Machinery 8vo,  2  50 

Ivatts,  E.  B.     Railway  Management  at  Stations 8vo,  *2  50 

Jacob,  A.,  and  Gould,  E.  S.     On  the  Designing  and  Construction  of 

Storage  Reservoirs.     (Science  Series  No.  6.) i6nio,  o  50 

Jamieson,  A.     Text  Book  on  Steam  and  Steam  Engines 8vo,  3  oo 

Elementary  Manual  on  Steam  and  the  Steam  Engine i2mo,  i  50 

Jannettaz,  E.     Guide  to  the  Determination  of  Rocks.     Trans,  by  G.  W. 

Plympton I2mo,  i  50 

Jehl,  F.     Manufacture  of  Carbons 8vo,  *4  oo 

Jennings,  A.  S.     Commercial  Paints  and  Painting.     (Westminster  Series.) 

8vo  (In  Press.) 

Jennison,  F.  H.     The  Manufacture  of  Lake  Pigments 8vo,  *3  oo 

Jepson,  G.     Cams  and  the  Principles  of  their  Construction 8vo,  *i  50 

Mechanical  Drawing 8vo  (In  Preparation.} 

Jockin,  W.     Arithmetic  of  the  Gold  and  Silversmith i2mo,  *i  oo 

Johnson,  G.  L.     Photographic  Optics  and  Color  Photography 8vo,  *3  oo 

Johnson,  J.  H.      Arc  Lamps  and  Accessory  Apparatus.     (Installation 

Manuals  Series.) i2mo,  *o  75 

Johnson,    T.    M.      Ship    Wiring    and    Fitting.       (Installation    Manuals 

Series) i2mo,  *o  75 

Johnson,  W.  H.     The  Cultivation  and  Preparation  of  Para  Rubber. .  .8vo,  *3  oo 

Johnson,  W.  McA.     The  Metallurgy  of  Nickel (In  Preparation.) 

Johnston,  J.  F.  W.,  and  Cameron,  C.     Elements  of  Agricultural  Chemistry 

and  Geology i2mo,  2  60 

Joly,  J.     Raidoactivity  and  Geology i2mo,  *3  oo 

Jones,  H.  C.     Electrical  Nature  of  Matter  and  Radioactivity i2mo,  *2  oo 

Jones,  M.  W.     Testing  Raw  Materials  Used  in  Paint i2mo,  *2  oo 

Jones,  L.,  and  Scard,  F.  I.     Manufacture  of  Cane  Sugar .8vo,  *5  oo 

Jordan,  L.  C.    Practical  Railway  Spiral i2mo,  Leather,  (In  Press.) 

Joynson,  F.  H.     Designing  and  Construction  of  Machine  Gearing. . .  .8vo,  2  oo 

Jiiptner,  H.  F.  V.     Siderology:  The  Science  of  Iron 8vo,  *5  oo 

Kansas  City  Bridge 4to,  6  oo 

Kapp,  G.     Alternate  Current  Machinery.     (Science  Series  No.  96.) .  i6mo,  o  50 

Electric  Transmission  of  Energy i2mo,  3  50 

Keim,  A.  W.     Prevention  of  Dampness  in  Buildings 8vo,  *2  oo 

Keller,  S.  S.     Mathematics  for  Engineering  Students.     i2mo,  half  leather. 

Algebra  and  Trigonometry,  with  a  Chapter  on  Vectors *i  75 

Special  Algebra  Edition *i  oo 

Plane  and  Solid  Geometry *i   25 

Analytical  Geometry  and  Calculus *2  oo 

Kelsey,  W.  R.     Continuous-current  Dynamos  and  Motors 8vo,  *2  50 

Kemble,  W.  T.,  and  Underbill,  C.  R.     The  Periodic  Law  and  the  Hydrogen 

Spectrum 8vo,  paper,  *o  50 

Kemp,  J.  £.     Handbook  of  Rocks 8vo.  *i  50 

Kendall,  E.    Twelve  Figure  Cipher  Code 4to,  *i2  50 

Kennedy,  A.  B.  W.,  and  Thurston,  R.  H.     Kinematics  of  Machinery. 

(Science  Series  No.  54.) i6mo,  o  50 

Kennedy,  A.  B.  W.,  Unwin,  W.  C.,  and  Idell,  F.  E.     Compressed  Air. 

(Science  Series  No.  106.) i6mo,  o  50 


D.  VAN  NOSTRAND  COMPANY'S  SHORT  TITLE  CATALOG      15 

Kennedy,  R.     Modern  Engines  and  Power  Generators.     Six  Volumes.   4to,  15  oo 

Single  Volumes each,  3  oo 

Electrical  Installations.     Five  Volumes 4to,  15  oo 

Single  Volumes each,  3  50 

Flying  Machines;  Practice  and  Design I2mo,  *2  oo 

Principles  of  Aeroplane  Construction 8vo,  *i  50 

Kennelly,  A.  E.     Electro-dynamic  Machinery 8vo,  I  50 

Kent,  W.     Strength  of  Materials.     (Science  Series  No.  41.) i6mo,  o  50 

Kershaw,  J.  B.  C.     Fuel,  Water  and  Gas  Analysis 8vo,  *2  50 

Electrometallurgy.     (Westminster  Series.) 8vo,  *2  oo 

The  Electric  Furnace  in  Iron  and  Steel  Production i2mo,  *i  50 

Kinzbrunner,  C.     Alternate  Current  Windings 8vo,  *i  50 

Continuous  Current  Armatures 8vo,  *i  50 

Testing  of  Alternating  Current  Machines 8vo,  *2  oo 

Kirkaldy,  W.  G.     David  Kirkaldy's  System  of  Mechanical  Testing 4to,  10  oo 

Kirkbride,  J.     Engraving  for  Illustration 8vo,  *i  50 

Kirkwood,  J.  P.     Filtration  of  River  Waters 4to,  7  50 

Klein,  J.  F.     Design  of  a  High-speed  Steam-engine 8vo,  *5  oo 

Physical  Significance  of  Entropy 8vo,  *i  50 

Kleinhans,  F.  B.     Boiler  Construction 8vo,  3  oo 

Knight,  R.-Adm.  A.  M.     Modern  Seamanship 8vo,  *7 .50 

Half  morocco *9  oo 

Knox,  W.  F.     Logarithm  Tables (In  Preparation.} 

Knott,  C.  G.,  and  Mackay,  J.  S.     Practical  Mathematics 8vo,  2  oo 

Koester,  F.     Steam-Electric  Power  Plants 4to,  *5  oo 

—  Hydroelectric  Developments  and  Engineering 4to,  *5  oo 

Koller,  T.     The  Utilization  of  Waste  Products* 8vo,  *3  50 

—  Cosmetics 8vo,  *2  50 

Kretchmar,  K.     Yarn  and  Warp  Sizing 8vo,  *4  oo 

Krischke,  A.     Gas  and  Oil  Engines i2mo,  *i  25 

Lambert,  T.     Lead  and  its  Compounds 8vo,  *3  50 

—  Bone  Products  and  Manures 8vo,  *3  oo 

Lamborn,  L.  L.     Cottonseed  Products 8vo,  *3  oo 

—  Modern  Soaps,  Candles,  and  Glycerin 8vo,  *7  50 

Lamprecht,  R.     Recovery  Work  After  Pit  Fires.     Trans,  by  C.  Salter .  .  8vo,  *4  oo 
Lanchester,  F.  W.     Aerial  Flight.     Two  Volumes.     8vo. 

Vol.    I.     Aerodynamics *6  oo 

—  Aerial  Flight.     Vol.  II.     Aerodonetics *6  oo 

Larner,  E.  T.     Principles  of  Alternating  Currents i2mo,  *i  25 

Larrabee,  C.  S.     Cipher  and  Secret  Letter  and  Telegraphic  Code i6mo,  o  60 

La  Rue,  B.  F.     Swing  Bridges.     (Science  Series  No.  107.) i6mo,  o  50 

Lassar-Cohn,  Dr.     Modern  Scientific  Chemistry.     Trans,  by  M.  M.  Patti- 

son  Muir i2mo,  *2  oo 

Latimer,  L.  H.,  Field,  C.  J.,  and  Howell,  J.  W.  Incandescent  Electric 

Lighting.  (Science  Series  No.  57.) i6mo,  o  50 

Latta,  M.  N.  Handbook  of  American  Gas-Engineering  Practice 8vo,  *4  50 

American  Producer  Gas  Practice 4*0,  *6  oo 

Leask,  A.  R.  Breakdowns  at  Sea i2mo,  2  oo 

Refrigerating  Machinery i2mo,  2  oo 

Lecky,  S.  T.  S.  "  Wrinkles  "  in  Practical  Navigation 8vo,  *8 


16      D.  VAN   NOSTRAND   COMPANY'S  SHORT  TITLE   CATALOG 

Le  Doux,  M.     Ice-Making  Machines.     (Science  Series  No.  46.) ....  i6mo,  o  50 

Leeds,  C.  C.     Mechanical  Drawing  foi  Trade  Schools oblong  4to, 

High  School  Edition *i  25 

Machinery  Trades  Edition *2  oo 

Lefe*vre,  L.     Architectural  Pottery.      Trans,  by  H.  K.  Bird  and  W.  M. 

Binns 4to,  *7  50 

Lehner,  S.     Ink  Manufacture.     Trans,  by  A.  Morris  and  H.  Robson  .  .  8vo,  *2  50 

Lemstrom,  S.     Electricity  in  Agriculture  and  Horticulture 8vo,  *i  50 

Le  Van,  W.  B.     Steam-Engine  Indicator.     (Science  Series  No.  78.) .  i6mo,  o  50 

Lewes,  V.  B.     Liquid  and  Gaseous  Fuels.     (Westminster  Series.).  ..  .8vo,  *2  oo 

Lewis,  L.  P.    Railway  Signal  Engineering 8vo,  *3  50 

Lieber,  B.  F.     Lieber's  Standard  Telegraphic  Code 8vo,  *io  oo 

Code.     German  Edition 8vo,  *io  oo 

Spanish  Edition 8vo,  *io  oo 

French  Edition 8vo,  *io  oo 

Terminal  Index 8vo,  *2  50 

Lieber's  Appendix folio,  *is  oo 

—  Handy  Tables 4to,  *2  50 

—  Bankers  and  Stockbrokers'  Code  and  Merchants  and  Shippers'  Blank 

Tables 8vo,  *i$  oo 

100,000,000  Combination  Code 8vo,  *io  oo 

Engineering  Code 8vo,  *i2  50 

Livermore,  V.  P.,  and  Williams,  J.     How  to  Become  a  Competent  Motor- 
man i2mo,  *i  oo 

Livingstone,  R.     Design  and  Construction  of  Commutators 8vo,  *2  25 

Lobben,  P.     Machinists'  and  Draftsmen's  Handbook 8vo,  2  50 

Locke,  A.  G.  and  C.  G.     Manufacture  of  Sulphuric  Acid 8vo,  10  oo 

Lockwood,  T.  D.     Electricity,  Magnetism,  and  Electro-telegraph  ....  8vo,  2  50 

Electrical  Measurement  and  the  Galvanometer i2mo,  o  75 

Lodge,  0.  J.     Elementary  Mechanics i2mo,  i  50 

—  Signalling  Across  Space  without  Wires 8vo,  *2  oo 

Loewenstein,  L.  C.,  and  Crissey,  C.  P.     Centrifugal  Pumps *4  50 

Lord,  R.  T.     Decorative  and  Fancy  Fabrics 8vo,  *3  50 

Loring,  A.  E.     A  Handbook  of  the  Electromagnetic  Telegraph i6mo,  o  50 

—  Handbook.     (Science  Series  No.  39.) i6mo,  o  50 

Low,  D.  A.    Applied  Mechanics  (Elementary) i6mo,  o  80 

Lubschez,  B   J.     Perspective (In  Press.) 

Lucke,  C.  E.«    Gas  Engine  Design 8vo,  *3  oo 

Power  Plants:  Design,  Efficiency,  and  Power  Costs.  2  vols.  (In  Preparation.) 

Lunge,  G.     Coal-tar  and  Ammonia.     Two  Volumes 8vo,  *i5  oo 

Manufacture  of  Sulphuric  Acid  and  Alkali.     Four  Volumes 8vo, 

Vol.     I.     Sulphuric  Acid.     In  two  parts *i$  oo 

Vol.    II.     Salt  Cake,  Hydrochloric  Acid  and  Leblanc  Soda.  In  two  parts  *is  oo 

Vol.  III.     Ammonia  Soda *io  oo 

Vol.  IV.   Electrolytic  Methods (In  Press.) 

Technical  Chemists'  Handbook i2mo,  leather,  *3  50 

Technical  Methods  of  Chemical  Analysis.     Trans,  by  C.  A.  Keane. 

in  collaboration  with  the  corps  of  specialists. 

Vol.   I.     In  two  parts 8vo,  *i5  oo 

Vol.  n.    In  two  parts 8vo,  *i8  oo 

Vol.  Ill (In  Preparation.) 


D.  VAN  NOSTRAND   COMPANY'S  SHORT  TITLE  CATALOG      17 

Lupton,  A.,  Parr,  G.  D.  A.,  and  Perkin,  H.     Electricity  as  Applied  to 

Mining 8vo,  *4  50 

Luquer,  L.  M.     Minerals  in  Rock  Sections 8vo,  *i  50 

Macewen,  H.  A.     Food  Inspection 8vo,  *2  50 

Mackenzie,  N.  F.     Notes  on  Irrigation  Works 8vo,  *2  50 

Mackie,  J.     How  to  Make  a  Woolen  Mill  Pay 8vo,  *2  oo 

Mackrow,  C.     Naval  Architect's  and  Shipbuilder's  Pocket-book. 

i6mo,  leather,  5  oo 

Maguire,  Wm.  R.     Domestic  Sanitary  Drainage  and  Plumbing 8vo,  4  oo 

Mallet,  A.     Compound  Engines.     Trans,  by  R.  R.  Buel.     (Science  Series 

No.  10.) i6mo, 

Mansfield,  A.  N.     Electro-magnets.     (Science  Series  No.  64.) i6mo,  o  50 

Marks,  E.  C.  R.     Construction  of  Cranes  and  Lifting  Machinery. .  . .  i2mo,  *i  50 

—  Construction  and  Working  of  Pumps i2mo,  *i  50 

—  Manufacture  of  Iron  and  Steel  Tubes I2mo,  *2  oo 

—  Mechanical  Engineering  Materials I2mo,  *i  oo 

Marks,  G.  C.     Hydraulic  Power  Engineering 8vo,  3  50 

—  Inventions,  Patents  and  Designs i2mo,  *i  oo 

Marlow,  T.  G.     Drying  Machinery  and  Practice 8vo,  *5  oo 

Marsh,  C.  F.     Concise  Treatise  on  Reinforced  Concrete 8vo,  *2  50 

—  Reinforced  Concrete  Compression  Member  Diagram.    Mounted  on 

Cloth  Boards *i  50 

Marsh,  C.  F.,  and  Dunn,  W.     Reinforced  Concrete 4to,  *5  oo 

Marsh,  C.  F.,  and  Dunn,  W.     Manual  of  Reinforced  Concrete  and  Con- 
crete Block  Construction i6mo,  morocco,  *2  50 

Marshall,  W.  J.,  and  Sankey,  H.  R.     Gas  Engines.     (Westminster  Series.) 

8vo,  *2  oo 

Martin.  G,     Triumphs  and  Wonders  of  Modern  Chemistry 8vo,  *2  oo 

Martin,   N.     Properties  and  Design  of  Reinforced  Concrete. 

(In  Press.)      K1 
Massie,  W.  W.,  and  Underbill,  C.  R.     Wireless  Telegraphy  and  Telephony. 

i2mo,  *i  oo 
Matheson,  D.     Australian  Saw-Miller's  Log  and  Timber  Ready  Reckoner. 

i2mo,  leather,  i  50 

Mathot,  R.  E.     Internal  Combustion  Engines 8vo,  *6  oo 

Maurice,  W.     Electric  Blasting  Apparatus  and  Explosives 8vo,  *3  50 

—  Shot  Firer's  Guide 8vo,  *i  50 

Maxwell,  J.  C.     Matter  and  Motion.     (Science  Series  No.  36.) i6mo,  o  50 

Maxwell,  W.  H.,  and  Brown,  J.  T.     Encyclopedia  of  Municipal  and  Sani- 
tary Engineering 4to,  *io  oo 

Mayer,  A.  M.     Lecture  Notes  on  Physics 8vo,  2  oo 

McCullough,  R.  S.     Mechanical  Theory  of  Heat 8vo,  3  50 

Mclntosh,  J.  G.     Technology  of  Sugar 8vo,  *4  50 

—  Industrial  Alcohol 8vo,  *3  oo 

Manufacture  of  Varnishes  and  Kindred  Industries.     Three  Volumes. 

8vo. 

Vol.     I.     Oil  Crushing,  Refining  and  Boiling *3  50 

Vol.    II.     Varnish  Materials  and  Oil  Varnish  Making *4  oo 

Vol.  HI.    Spirit  Varnishes  and  Materials *4  So 

McKnight,  J.  D.,  and  Brown,  A.  W.     Marine  Multitubular  Boilers *i  50 


18     D.  VAN   NOSTRAND   COMPANY'S   SHORT  TITLE  CATALOG 

McMaster,  J.  B.    Bridge  and  Tunnel  Centres.     (Science  Series  No.  20.) 

i6mo,  o  50 

McMechen,  F.  L.      Tests  for  Ores,  Minerals  and  Metals i2mo,  *i  oo 

McNeill,  B.     McNeill's  Code 8vo,  *6  oo 

McPherson,  J.  A.     Water- works  Distribution 8vo,  2  50 

Melick,  C.  W.     Dairy  Laboratory  Guide i2mo,  *i  25 

Merck,  E.     Chemical  Reagents;  Their  Purity  and  Tests 8vo,  *i  50 

Merritt,  Wm.  H.     Field  Testing  for  Gold  and  Silver i6mo,  leather,  i  50 

Messer,  W.  A.    Railway  Permanent  Way 8vo,  (In  Press.) 

Meyer,  J.  G.  A.,  and  Pecker,  C.  G.     Mechanical  Drawing  and  Machine 

Design 4to,  5  oo 

Michell,  S.     Mine  Drainage 8vo,  10  oo 

Mierzinski,  S.     Waterproofing  of  Fabrics.     Trans,  by  A.  Morris  and  H, 

Robson 8vo,  *2  50 

Miller,  E.  H.     Quantitative  Analysis  for  Mining  Engineers 8vo,  *i  50 

Miller,  G.  A.     Determinants.     (Science  Series  No.  105.) i6mo, 

Milroy,  M.  E.  W.     Home  Lace-making i2mo,  *i  oo 

Minifie,  W.     Mechanical  Drawing 8vo,  *4  oo 

Mitchell,  C.  A.,  and  Prideaux,  R.  M.     Fibres  Used  in  Textile  and  Allied 

Industries 8vo,  *3  oo 

Modern  Meteorology i2mo,  i  50 

Monckton,  C.  C.  F.     Radiotelegraphy.     (Westminster  Series.) 8vo,  *2  oo 

Monteverde,  R.  D.     Vest  Pocket  Glossary  of  English-Spanish,  Spanish- 
English  Technical  Terms 64010,  leather,  *i  oo 

Moore,  E.  C.  S.     New  Tables  for  the  Complete  Solution  of  Ganguillet  and 

Kutter's  Formula 8vo,  *5  oo 

Morecroft,  J.  H.,  and  Hehre,  F.  W.     Short  Course  in  Electrical  Testing. 

8vo,  *i  50 

Moreing,  C.  A.,  and  Neal,  T.    New  General  and  Mining  Telegraph  Code,  8vo,  *s  oo 

Morgan,  A.  P.     Wireless  Telegraph  Apparatus  for  Amateurs i2mo,  *i  50 

Moses,  A.  J.     The  Characters  of  Crystals 8vo,  *2  oo 

Moses,  A.  J.,  and  Parsons,  C.  L.     Elements  of  Mineralogy 8vo,  *2  50 

Moss,  S.  A.  Elements  of  Gas  Engine  Design.  (Science  Series  No.i2i.)i6mo,  o  50 

The  Lay-out  of  Corliss  Valve  Gears.   (Science  Series  No.  119.).  i6mo,  o  50 

Mulford,  A.  C.    Boundaries  and  Landmarks (In  Press.) 

Mullin,  J.  P.     Modern  Moulding  and  Pattern-making i2mo,  2  50 

Munby,  A.  E.     Chemistry  and  Physics  of  Building  Materials.     (Westmin- 
ster Series.) 8vo,  *2  oo 

Murphy,  J.  G.     Practical  Mining i6mo,  i  oo 

Murray,  J.  A.     Soils  and  Manures.     (Westminster  Series.) Svo,  *2  oo 

Naquet,  A.     Legal  Chemistry i2mo,  2  oo 

Nasmith,  J.     The  Student's  Cotton  Spinning Svo,  3^00 

Recent  Cotton  Mill  Construction i2mo,  2^00 

Neave,  G.  B.,  and  Heilbron,  I.  M.    Identification  of  Organic  Compounds.  fe  |3 

i2mo,  *i  25 

Neilson,  R.  M.     Aeroplane  Patents Svo,  *2  oo 

Nerz,  F.     Searchlights.     Trans,  by  C.  Rodgers Svo,  *3  oo 

Nesbit,  A.  F.    Electricity  and  Magnetism (In  Preparation.) 

Neuberger,  H.,  and  Noalhat,  H.     Technology  of  Petroleum.     Trans,  by  J. 

G.  Mclntosh Svo,  *io "oo 


D.  VAN  NOSTRAND   COMPANY'S  SHORT  TITLE  CATALOG      19 

Newall,  J.  W.     Drawing,  Sizing  and  Cutting  Bevel-gears 8vo,  i  50 

Nicol,  G.     Ship  Construction  and  Calculations 8vo,  *4  50 

Nipher,  F.  E.     Theory  of  Magnetic  Measurements I2mo,  i  oo 

Nisbet,  H.     Grammar  of  Textile  Design 8vo,  *3  oo 

Nolan,  H.    The  Telescope.     (Science  Series  No.  51.) i6mo,  o  50 

Noll,  A.     How  to  Wire  Buildings i2mo,  i  50 

North,  H.  B.    Laboratory  Notes  of  Experiments  and  General  Chemistry. 

(7n  Press.) 

Nugent,  E.     Treatise  on  Optics i2mo,  i  50 

O'Connor,  H.  The  Gas  Engineer's  Pocketbook i2mo,  leather,  3  50 

Petrol  Air  Gas. i2mo,  *o  75 

Ohm,  G.  S.,  and  Lockwood,  T.  D.  Galvanic  Circuit.  Translated  by 

William  Francis.  (Science  Series  No.  102.) ••.•••  i6mo,  o  50 

Olsen,  J.  C.  Text-book  of  Quantitative  Chemical  Analysis 8vo,  *4  oo 

Olsson,  A.  Motor  Control,  in  Turret  Turning  and  Gun  Elevating.  (U.  S. 

Navy  Electrical  Series,  No.  i.) i2mo,  paper,  *o  50 

Oudin,  M.  A.  Standard  Polyphase  Apparatus  and  Systems 8vo,  *3  oo 

Pakes,  W.  C.  C.,  and  Nankivell,  A.  T.    The  Science  of  Hygiene.  .8vo,  *i  75 

Palaz,  A.     Industrial  Photometry.     Trans,  by  G.  W.  Patterson,  Jr. . .  8vo,  *4  oo 

Pamely,  C.     Colliery  Manager's  Handbook 8vo,  *io  oo 

Parr,  G.  D.  A.     Electrical  Engineering  Measuring  Instruments 8vo,  *3  50 

Parry,  E.  J.     Chemistry  of  Essential  Oils  and  Artificial  Perfumes ....  8vo,  *5  oo 

Foods  and  Drugs.     Two  Volumes 8vo, 

Vol.    I.     Chemical  and  Microscopical  Analysis  of  Foods  and  Drugs.  *7  5° 

Vol.  H.     Sale  of  Food  and  Drugs  Act *3  oo 

Parry,  E.  J.,  and  Coste,  J.  H.     Chemistry  of  Pigments 8vo,  *4  50 

Parry,  L.  A.     Risk  and  Dangers  of  Various  Occupations 8vo,  *3  oo 

Parshall,  H.  F.,  and  Hobart,  H.  M.     Armature  Windings 4to,  *7  50 

—  Electric  Railway  Engineering 4to,  *io  oo 

Parshall,  H.  F.,  and  Parry,  E.     Electrical  Equipment  of  Tramways (In  Press.) 

Parsons,  S.  J.     Malleable  Cast  Iron 8vo,  *2  50 

Partmgton,  J.  R.    Higher  Mathematics  for  Chemical  Students.  .i2mo,  *2  oo 

Passmore,  A.  C.     Technical  Terms  Used  in  Architecture 8vo,  *3  50 

Paterson,  G.  W.  L.    Wiring  Calculations i2mo,  *2  oo 

Patterson,  D.     The  Color  Printing  of  Carpet  Yarns 8vo,  *3  50 

Color  Matching  on  Textiles 8vo,  *j  oo 

The  Science  of  Color  Mixing 8vo,  *3  oo 

Paulding,  C.  P.     Condensation  of  Steam  in  Covered  and  Bare  Pipes. 

8vo,  *2  oo 

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Payne,   D.   W.     Iron  Founders'   Handbook (In   Press.) 

Peddle,  R.  A.    Engineering  and  Metallurgical  Books i2mo, 

Peirce,  B.     System  of  Analytic  Mechanics 4to,  10  oo 

Pendred,  V.     The  Railway  Locomotive.     (Westminster  Series.) 8vo,  *2  oo 

Perkin,  F.  M.     Practical  Methods  of  Inorganic  Chemistry i2mo,  *i  oo 

Perrigo,  O.  E.     Change  Gear  Devices 8vo,  i  oo 

Perrine,  F.  A.  C.     Conductors  for  Electrical  Distribution 8vo,  *3  50 

Perry,  J.     Applied  Mechanics 8vo,  *2  50 

Petit,  G.     White  Lead  and  Zinc  White  Paints 8vo,  *i  50 


20      D.  VAN   NOSTRAND   COMPANY'S  SHORT  TITLE   CATALOG 

Petit,  R.     How  to  Build  an  Aeroplane.     Trans,  by  T.  O'B.  Hubbard,  and 

J.  H.  Ledeboer 8vo,  *i  50 

Pettit,  Lieut.  J.  S.     Graphic  Processes.     (Science  Series  No.  76.) . . .  i6mo,  o  50 
Philbrick,  P.  H.     Beams  and  Girders.     (Science  Series  No.  88.) . . .  i6mo, 

Phillips,  J.     Engineering  Chemistry 8vo,  *4  50 

Gold  Assaying 8vo,  *2  50 

Dangerous  Goods 8vo,  3  50 

Phin,  J.     Seven  Follies  of  Science i2mo,  *i  25 

Pickworth,  C.  N.     The  Indicator  Handbook.     Two  Volumes.  .i2mo,  each,  i  50 

Logarithms  for  Beginners i2mo,  boards,  o  50 

The  Slide  Rule i2mo,  i  oo 

Plattner's  Manual  of  Blow-pipe  Analysis.    Eighth  Edition,  revised.    Trans. 

by  H.  B.  Cornwall 8vo,  *4  oo 

Plympton,  G.  W.    The  Aneroid  Barometer.    (Science  Series  No.  35.)   i6mo,  o  50 

How  to  become  an  Engineer.      (Science  Series  No.  100.) i6mo,  o  50 

Van  Nostrand's  Table  Book.     (Science  Series  No.  104.) i6mo,  o  50 

Pochet,  M.  L.     Steam  Injectors.     Translated  from  the  French.     (Science 

Series  No.  29.) i6mo,  o  50 

Pocket  Logarithms  to  Four  Places.     (Science  Series  No.  65.) i6mo,  o  50 

leather,  i  oo 

Polleyn,  F.     Dressings  and  Finishings  for  Textile  Fabrics 8vo,  *3  oo 

Pope,  F.  L.     Modern  Practice  of  the  Electric  Telegraph 8vo,  i  50 

Popple  well,  W.  C.  Elementary  Treatise  on  Heat  and  Heat  Engines.  .  i2mo,  *3  oo 

—  Prevention  of  Smoke 8vo,  *3  50 

—  Strength  of  Materials 8vo,  *i  75 

Porter,  J.  R.     Helicopter  Flying  Machine i2mo,  *i  25 

Potter,  T.     Concrete 8vo,  *3  oo 

Potts,  H.  E.     Chemistry  of  the  Rubber  Industry.     (Outlines  of  Indus- 
trial Chemistry) 8vo,  *2  oo 

Practical  Compounding  of  Oils,  Tallow  and  Grease ............  8vo,  *3  50 

Practical  Iron  Founding i2mo,  i  50 

Pratt,  K.    Boiler  Draught i2mo,  *i  25 

Pray,  T.,  Jr.     Twenty  Years  with  the  Indicator 8vo,  2  50 

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Preece,  W.  H.     Electric  Lamps (In  Press.} 

Prelini,  C.     Earth  and  Rock  Excavation 8vo,  *3  oo 

Graphical  Determination  of  Earth  Slopes 8vo,  *2  oo 

Tunneling.    New  Edition 8vo,  *3  oo 

Dredging.    A  Practical  Treatise 8vo,  *3  oo 

Prescott,  A.  B.     Organic  Analysis 8vo,  5  oo 

Prescott,  A.  B.,  and  Johnson,  0.  C.     Qualitative  Chemical  Analysis. .  .8vo,  *3  50 
Prescott,  A.  B.,  and  Sullivan,  E.  C.     First  Book  in  Qualitative  Chemistry. 

I2mo,  *i  50 

Prideaux,  E.  B.  R.     Problems  in  Physical  Chemistry 8vo,  *2  oo 

Pritchard,*0.  G.     The  Manufacture  of  Electric-light  Carbons.  .8vo,  paper,  *o  60 
Pullen,  W.  W.  F.     Application  of  Graphic  Methods  to  the  Design  of 

Structures i2mo,  *2  50 

Injectors:  Theory,  Construction  and  Working i2mo,  *i  50 

Pulsifer,  W.  H.     Notes  for  a  History  of  Lead 8vo,  4  oo 

Purchase,  W.  R.     Masonry i2mo,  *3  oo 


D.   VAN   NOSTRAND   COMPANY'S  SHORT  TITLE   CATALOG      21 

Putsch,  A.     Gas  and  Coal-dust  Firing 8vo,  *3  oo 

Pynchon,  T.  R.     Introduction  to  Chemical  Physics 8vo,  3  oo 

Rafter  G.  W*     Mechanics  of  Ventilation.     (Science  Series  No.  33.) .  i6mo,  o  50 

Potable  Water,     (Science  Series  No.  103.) i6mc  50 

Treatment  of  Septic  Sewage.     (Science  Series  No.  118.). .  . .  i6mo  50 

Rafter,  G.  W.,  and  Baker,  M.  N.     Sewage  Disposal  in  the  United  States. 

4to,  *6  oo 

Raikes,  H.  P.     Sewage  Disposal  Works 8vo,  *4  oo 

Railway  Shop  Up-to-Date 4to,  2  oo 

Ramp,  H.  M.     Foundry  Practice (In  Press.) 

Randall,  P.  M.     Quartz  Operator's  Handbook I2mo,  2  oo 

Randau,  P.     Enamels  and  Enamelling 8 vo,  *4  oo 

Rankine,  W.  J.  M.     Applied  Mechanics 8vo,  5  oo 

Civil  Engineering 8vo,  6  50 

Machinery  and  Millworfc 8vo,  5  oo 

—  The  Steam-engine  and  Other  Prime  Movers 8vo,  5  oo 

-  Useful  Rules  and  Tables 8vo,  4  oo 

Rankine,  W.  J.  M.,  and  Bamber,  E.  F.     A  Mechanical  Text-book. ...  8vo,  350 
Raphael,  F.  C.     Localization  of  Faults  in  Electric  Light  and  Power  Mains. 

8vo,  *3  oo 

Rasch,  E.    Electric  Arc.    Trans,  by  K.  Tornberg (In  Press.) 

Rathbone,  R.  L.  B.     Simple  Jewellery 8vo,  *2  oo 

Rateau,  A.     Flow  of  Steam  through  Nozzles  and  Orifices.     Trans,  by  H. 

B.  Brydon 8vo,  *i  50 

Rausenberger,  F.     The  Theory  of  the  Recoil  of  Guns 8vo,  *4  50 

Rautenstrauch,  W.    Notes  on  the  Elements  of  Machine  Design. 8 vo,  boards,  *i  50 
Rautenstrauch,  W.,  and  Williams,  J.  T.     Machine  Drafting  and  Empirical 
Design. 

Part   I.  Machine  Drafting 8vo,  *i  25 

Part  II.  Empirical  Design (In  Preparation.) 

Raymond,  E.  B.     Alternating  Current  Engineering i2mo,  *2  50 

Rayner,  H.     Silk  Throwing  and  Waste  Silk  Spinning 8vo,  *2  50 

Recipes  for  the  Color,  Paint,  Varnish,  Oil,  Soap  and  Drysaltery  Trades .  8vo,  *3  50 

Recipes  for  Flint  Glass  Making i2mo,  *4  50 

Redfern,  J.  B.    Bells,  Telephones  (Installation  Manuals  Series)  i6mo, 

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Redwood,  B.     Petroleum.     (Science  Series  No.  92.) i6mo,  o  50 

Reed's  Engineers'  Handbook 8vo,  *5  oo 

Key  to  the  Nineteenth  Edition  of  Reed's  Engineers'  Handbook . .  8vo,  *3  oo 

Useful  Hints  to  Sea-going  Engineers i2mo,  i  50 

Marine  Boilers i2mo,  2  oo 

Reinhardt,  C.  W.     Lettering  for  Draftsmen,  Engineers,  and  Students. 

oblong  4to,  boards,  i  oo 

-  The  Technic  of  Mechanical  Drafting oblong  4to,  boards,  *i  oo 

Reiser,  F.     Hardening  and  Tempering  of  Steel.     Trans,  by  A.  Morris  and 

H.  Robson i2mo,  *2  50 

Reiser,  N.  Faults  in  the  Manufacture  of  Woolen  Goods.  Trans,  by  A. 

Morris  and  H.  Robson 8vo,  *2  50 

Spinning  and  Weaving  Calculations 8vo,  *5  oo 

Renwick,  W.  G.  Marble  and  Marble  Working 8vo,  5  oo 


22      D.  VAN   NOSTRAND   COMPANY'S  SHORT  TITLE  CATALOG 

Reynolds,   0.,  and  Idell,  F.   E.     Triple   Expansion  Engines.     (Science 

Series  No.  99.) i6mo,  o  50 

Rhead,  G.  F.     Simple  Structural  Woodwork i2mo,  *i  oo 

Rice,  J.  M.,  and  Johnson,  W.  W.     A  New  Method  of  Obtaining  the  Differ- 
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Richards,  W.  A.  and  North,  H.  B.     Manual  of  Cement  Testing.  (In  Press.} 

Richardson,  J.     The  Modern  Steam  Engine 8vo,  *3  50 

Richardson,  S.  S.     Magnetism  and  Electricity i2mo,  *2  oo 

Rideal,  S.     Glue  and  Glue  Testing 8vo,  *4  oo 

Rings,  F.     Concrete  in  Theory  and  Practice i2mo,  *2  50 

Ripper,  W.     Course  of  Instruction  in  Machine  Drawing folio,  *6  oo 

Roberts,  F.  C.     Figure  of  the  Earth.     (Science  Series  No.  79.) i6mo,  o  50 

Roberts,  J.,  Jr.     Laboratory  Work  in  Electrical  Engineering 8vo,  *2  oo 

Robertson,  L.  S.     Water-tube  Boilers 8vo,  3  oo 

Robinson,  J.  B.     Architectural  Composition 8vo,  *2  50 

Robinson,  S.  W.     Practical  Treatise  on  the  Teeth  of  Wheels.     (Science 

Series  No.  24.) i6mo,  o  50 

Railroad  Economics.     (Science  Series  No.  59.) i6mo,  o  50 

Wrought  Iron  Bridge  Members.     (Science  Series  No.  60.) i6mo,  050 

Robson,  J.  H.     Machine  Drawing  and  Sketching 8vo,  *i  50 

Roebling,  J   A.     Long  and  Short  Span  Railway  Bridges folio,  25  oo 

Rogers,  A.     A  Laboratory  Guide  of  Industrial  Chemistry i2mo,  *i  50 

Rogers,  A.,  and  Aubert,  A.  B.     Industrial  Chemistry. 8vo,  *5  oo 

Rogers,  F.     Magnetism  of  Iron  Vessels.     (Science  Series  No.  30.) .  .  i6mo,  o  50 

Rohland,  P.     Colloidal  and  Cyrstalloidal   State  of  Matter.     Trans,  by  •...] 

W.  J.  Britland  and  H.  E.  Potts i2mo,  *i  25 

Rollins,  W.    Notes  on  X-Light 8vo,  *5  oo 

Rollinson,  C.     Alphabets Oblong,  .i2mo,  (In  Press.) 

Rose,  J.     The  Pattern-makers'  Assistant 8vo,  2  50 

Key  to  Engines  and  Engine-running i2mo,  2  50 

Rose,  T.  K.     The  Precious  Metals.     (Westminster  Series.) 8vo,  *2  oo 

Rosenhain,  W.     Glass  Manufacture.     (Westminster  Series.) 8vo,  *2  oo 

Ross,  W.  A.     Plowpipe  in  Chemistry  and  Metallurgy i2mo,  *2  oo 

Rossiter,  J.  T.     Steam  Engines.     (Westminster  Series.) 8vo  (In  Press.*) 

Pumps  and  Pumping  Machinery.     (Westminster  Series.).. 8 vo  (In  Press.) 

Roth.     Physical  Chemistry 8vo,  *2  oo 

Rouillion,  L.     The  Economics  of  Manual  Training 8vo,  2  oo 

Rowan,  F.  J.     Practical  Physics  of  the  Modern  Steam-boiler 8vo,  7  50 

Rowan,   F.   J.,   and  Idell,   F.   E.     Boiler  Incrustation  and  Corrosion. 

(Science  Series  No.  27.) i6mo,  o  50 

Roxburgh,  W.     General  Foundry  Practice 8vo,  *3  50 

Ruhmer,  E.     Wireless  Telephony.     Trans,  by  J.  Erskine-Murray. ..  .8vo,  *3  50 

Russell,  A.     Theory  of  Electric  Cables  and  Networks 8vo,  *3  oo 

Sabine,  R.     History  and  Progress  of  the  Electric  Telegraph i2mo,  i  25 

Saeltzer  "A.     Treatise  on  Acoustics I2mo,  i  oo 

Salomons,  D.     Electric  Light  Installations.     i2mo. 

Vol.    I.     The  Management  of  Accumulators 2  50 

Vol.  II.     Apparatus , 2  25 

Vol.  III.     Applications i  50 

Sanford,  P.  G.     Nitro-explosives 8vo,  *4  oo 


D.  VAN   NOSTRAND   COMPANY'S   SHORT  TITLE  CATALOG     23 

Saunders,  C.  H.     Handbook  of  Practical  Mechanics i6mo,  i  oo 

leather,  i  25 

Saunnier,  C.     Watchmaker's  Handbook. i2mo,  3  oo 

Sayers,  H.  M.     Brakes  for  Tram  Cars 8vo,  *i  25 

Scheele,  C.  W.     Chemical  Essays 8vo,  *2  oo 

Schellen,  H.     Magneto-electric  and  Dynamo-electric  Machines 8vo,  5  oo 

Scherer,  R.     Casein.     Trans,  by  C.  Salter 8vo,  *3  oo 

Schidrowitz,  P.    Rubber,  Its  Production  and  Industrial  Uses  . , 8vo,  *s  oo 

Schindler,  K.    Iron  and  Steel  Construction  Works. 

Schmall,  C.  N.     First  Course  in  Analytic  Geometry,  Plane  and  Solid. 

i2mo,  half  leather,  *i  75 

Schmall,  C.  N.,  and  Shack,  S.  M.     Elements  of  Plane  Geometry i2mo,  *i  25 

Schmeer,  L.     Flow  of  Water 8vo,  *3  oo 

Schumann,  F.     A  Manual  of  Heating  and  Ventilation i2mo,  leather,  i  50 

Schwarz,  E.  H.  L.     Causal  Geology 8vo,  *2  50 

Schweizer,  V.,  Distillation  of  Resins 8vo,  *3  50 

Scott,  W.  W.     Qualitative  Analysis.     A  Laboratory  Manual 8vo,  *i  50 

Scribner,  J.  M.     Engineers'  and  Mechanics'  Companion  .  . .  i6mo,  leather,  i  50 

Searle,  A.  B.     Modern  Brickmaking 8vo,  *5  oo 

Searle,  G.  M.     "  Sumners'  Method."     Condensed  and  Improved.    (Science 

Series  No.  124.) i6mo,  o  50 

Seaton,  A.  E.     Manual  of  Marine  Engineering 8vo,  6  oo 

Seaton,  A.  E.,  and  Rounthwaite,  H.  M.     Pocket-book  of  Marine  Engineer- 
ing  ' i6mo,  leather,  3  oo 

Seeligmann,  T.,  Torrilhon,  G.  L.,  and  Falconnet,  H.     India  Rubber  and 

Gutta  Percha.     Trans,  by  J.  G.  Mclntosh 8vo,  *s  oo 

Seidell,  A.     Solubilities  of  Inorganic  and  Organic  Substances 8vo,  *3  oo 

Sellew,  W.  H.     Steel  Rails 4to  (In  Press.) 

Senter,  G.     Outlines  of  Physical  Chemistry i2mo,  *i  75 

Textbook  of  Inorganic  Chemistry izmo,  *i  75 

Sever,  G.  F.     Electric  Engineering  Experiments 8vo,  boards,  *i  oo 

Sever,  G.  F.,  and  Townsend,  F.     Laboratory  and  Factory  Tests  in  Electrical, 

Engineering 8vo,  *2  50 

Sewall,  C.  H.     Wireless  Telegraphy 8vo,  *2  oo 

Lessons  in  Telegraphy i2mo,  *i  oo 

Sewell,  T.     Elements  of  Electrical  Engineering 8vo,  *3  oo 

The  Construction  of  Dynamos 8mo,  *3  oo 

Sexton,  A.  H.     Fuel  and  Refractory  Materials i2mo,  *2  50 

— —  Chemistry  of  the  Materials  of  Engineering i2mo,  *2  50 

Alloys  (Non- Ferrous) 8vo,  *3  oo 

The  Metallurgy  of  Iron  and  Steel 8vo,  *6  50 

Seymour,  A.     Practical  Lithography 8vo,  *2  50 

Modern  Printing  Inks 8vo,  *2  oo 

Shaw,  Henry  S.  H.     Mechanical  Integrators.     (Science  Series  No.  83.) 

i6mo,  o  50 

Shaw,  P.  E.     Course  of  Practical  Magnetism  and  Electricity 8vo,  *i  oo 

Shaw,  S.     History  of  the  Staffordshire  Potteries 8vo,  *3  oo 

Chemistry  of  Compounds  Used  in  Porcelain  Manufacture &vo,  *5  oo 

Shaw,  W.  N.    Forecasting  Weather 8vo,  *3  50 

Sheldon,  S.,  and  Hausmann,  E.    Direct  Current  Machines i2mo,  *2  50 

Alternating  Current  Machines 12010,  *2  50 


24     D.  VAN   NOSTRAND   COMPANY'S   SHORT  TITLE   CATALOG 

Sheldon,  S.,  and  Hausmann,  E.     Electric  Traction  and  Transmission 

Engineering i2mo,  *2  50 

Sherriff,  F.  F.     Oil  Merchants'  Manual i2mo,  *3  50 

Shields,  J.  E.     Notes  on  Engineering  Construction i2mo,  i  50 

Shock,  W.  H.     Steam  Boilers -4to,  half  morocco,  15  oo 

Shreve,  S.  H.     Strength  of  Bridges  and  Roofs 8vo,  3  50 

Shunk,  W.  F.     The  Field  Engineer i2mo,  morocco,  2  50 

Simmons,  W.  H.,  and  Appleton,  H.  A.    Handbook  of  Soap  Manufacture. 

8vo,  *3  oo 

Simmons,  W.  H.,  and  Mitchell,  C.  A.     Edible  Fats  and  Oils 8vo,  *3  oo 

Simms,  F.  W.     The  Principles  and  Practice  of  Leveling 8vo,  2  50 

Practical  Tunneling 8vo,  7  50 

Simpson,  G.    The  Naval  Constructor i2mo,  morocco,  *5  oo 

Simpson,   W.     Foundations 8vo,    (In   Press.) 

Sinclair,  A.     Development  of  the  Locomotive  Engine  .  . .  8vo,  half  leather,  5  oo 

Sinclair,  A.     Twentieth  Century  Locomotive 8vo,  half  leather,  *5  oo 

Sindall,  R.  W.     Manufacture  of  Paper.     (Westminster  Series.) 8vo,  *2  oo 

Sloane,  T.  O'C.     Elementary  Electrical  Calculations i2mo,  *2  oo 

Smith,  C.  A.  M.     Handbook  of  Testing,  MATERIALS 8vo,  *2  50 

Smith,  C.  A.  M.,  and  Warren,  A.  G.    New  Steam  Tables 8vo, 

Smith,  C.  F.     Practical  Alternating  Currents  and  Testing 8vo,  *2  50 

Practical  Testing  of  Dynamos  and  Motors 8vo,  *2  oo 

Smith,  F.  E.     Handbook  of  General  Instruction  for  Mechanics.  .  .  .  i2mo,  i  50 

Smith,  J.  C.     Manufacture  of  Paint • 8vo,  *3  oo 

Smith,  R.  H.    Principles  of  Machine  Work i2mo,  *3^oo 

Elements  of  Machine  Work i2mo,  *2  oo 

Smith,  W.     Chemistry  of  Hat  Manufacturing i2mo,  *3  oo 

Snell,  A.  T.     Electric  Motive  Power 8vo,  *4  oo 

Snow,  W.  G.     Pocketbook  of  Steam  Heating  and  Ventilation.    (In  Press.) 
Snow,  W.  G.,  and  Nolan,  T.     Ventilation  of  Buildings.     (Science  Series 

No.  5.) i6mo,  o  50 

Soddy,  F.     Radioactivity 8vo,  *3  oo 

Solomon,  M.     Electric  Lamps.     (Westminster  Series.) 8vo,  *2  oo 

Sothern,  J.  W.     The  Marine  Steam  Turbine 8vo,  *5  oo 

Southcombe,  J.  E.    Paints,  Oils  and  Varnishes.     (Outlines  of  Indus- 
trial Chemistry.) 8vo,   (In  Press.) 

Soxhlet,  D.  H.     Dyeing  and  Staining  Marble.     Trans,  by  A.  Morris  and 

H.  Robson 8vo,  *2  50 

Spang,  H.  W.     A  Practical  Treatise  on  Lightning  Protection i2mo,  i  oo 

Spangenburg,    L.     Fatigue    of    Metals.     Translated    by    S.    H.    Shreve. 

(Science  Series  No.  23.) i6mo,  o  50 

Specht,  G.  J.,  Hardy,  A.  S.,  McMaster,  J.B  .,  and  Walling.     Topographical 

Surveying.     (Science  Series  No.  72.). i6mo,  o  50 

Speyers,  C.  L.     Text-book  of  Physical  Chemistry 8vo,  *2  25 

Stahl,  A.  W.     Transmission  of  Power.     (Science  Series  No.  28.) . . .  i6mo, 

Stahl,  A..  W.,  and  Woods,  A.  T.     Elementary  Mechanism i2mo,  *2  oo 

Staley,  C.,  and  Pierson,  G.  S.     The  Separate  System  of  Sewerage. . .  .8vo,  *3  oo 

Standage,  H.  C.     Leatherworkers'  Manual 8vo,  *3  50 

Sealing  Waxes,  Wafers,  and  Other  Adhesives 8vo,  *2  oo 

Agglutinants  of  all  Kinds  for  all  Purposes I2mo,  *3  50 

Stansbie,  J.  H.     Iron  and  Steel.     (Westminster  Series.) 8vo,  *2  oo 


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Steinman,  D.  B.     Suspension  Bridges  and  Cantilevers.     (Science  Series 

No.  127) o  50 

Stevens,  H.  P.     Paper  Mill  Chemist i6mo,  *2  50 

Stevenson,  J.  L.     Blast-Furnace  Calculations I2mo,  leather,  *2  oo 

Stewart,  A.     Modern  Polyphase  Machinery i2mo,  *2  oo 

Stewart,  G.     Modern  Steam  Traps i2mo,  *i  25 

Stiles,  A.     Tables  for  Field  Engineers i2mo,  i  oo 

Stillman,  P.     Steam-engine  Indicator i2mo,  i  oo 

Stodola,  A.     Steam  Turbines.     Trans,  by  L.  C.  Loewenstein 8vo,  *5  oo 

Stone,  H.     The  Timbers  of  Commerce 8vo,  3  50 

Stone,  Gen.  R.    New  Roads  and  Road  Laws I2mo,  i  oo 

Stopes,  M.     Ancient  Plants 8vo,  *2  oo 

The  Study  of  Plant  Life 8vo,  *2  oo 

Stumpf,  Prof.    Una-Flow  of  Steam  Engine (In  Press.) 

Sudborough,  J.  J.,  and  James,  T.  C.     Practical  Organic  Chemistry.  .  i2mo,  *2  oo 

Suffling,  E.  R.     Treatise  on  the  Art  of  Glass  Painting 8vo,  *3  50 

Swan,  K.     Patents,  Designs  and  Trade  Marks.      (Westminster  Series.).8vo,  *2  oo 

Sweet,  S.  H.     Special  Report  on  Coal 8vo,  3  oo 

Swinburne,  J.,  Wordingham,  C.  H.,  and  Martin,  T.  C.     Eletcric  Currents. 

(Science  Series  No.  109.) i6mo,  o  50 

Swoope,  C.  W.     Practical  Lessons  in  Electricity i2mo,  *2  oo 

Tailfer,  L.     Bleaching  Linen  and  Cotton  Yarn  and  Fabrics 8vo,  *5  oo 

Tate,  J.  S.     Surcharged  and  Different  Forms  of  Retaining-walls.     (Science 

Series  No.  7.) i6mo,  o  50 

Taylor,  E.  N.     Small  Water  Supplies i2mo,  *2  oo 

Templeton,  W.     Practical  Mechanic's  Workshop  Companion. 

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Terry,  H.  L.     India  Rubber  and  its  Manufacture.     (Westminster  Series.) 

8vo,  *2  oo 
Thayer,  H.  R.     Structural  Design.    8vo. 

Vol.     I.    Elements  of  Structural  Design *2  oo 

Vol.    H.    Design  of  Simple  Structures (In  Preparation,) 

Vol.  III.    Design  of  Advanced  Structures (In  Preparation.) 

Thiess,  J.  B.  and  Joy,  G.  A.    Toll  Telephone  Practice 8vo,  *3  50 

Thorn,  C.,  and  Jones,  W.  H.     Telegraphic  Connections oblong  i2mo,  i  50 

Thomas,  C.  W.     Paper-makers'  Handbook (In  Press.) 

Thompson,  A.  B.     Oil  Fields  of  Russia 4to,  *7  50 

Petroleum  Mining  and  Oil  Field  Development 8vo,  *5  oo 

Thompson,  E.  P.     How  to  Make  Inventions 8vo,  o  50 

Thompson,  S.  P.     Dynamo  Electric  Machines.     (Science  Series  No.  75.) 

i6mo,  o  50 

Thompson,  W.  P.     Handbook  of  Patent  Law  of  All  Countries i6mo,  i  50 

Thomson,  G.  S.     Milk  and  Cream  Testing i2mo,  *i  75 

Modern  Sanitary  Engineering,  House  Drainage,  etc.  8vo,  (In  Press.) 

Thornley,  T.     Cotton  Combing  Machines 8vo,  *3  oo 

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First  Year *i  50 

Second  Year *2  50 

Third  Year *2  50 

Thurso,  J.  W.     Modern  Turbine  Practice 8vo,  *4  oo 


26     D.   VAN   NOSTRAND   COMPANY'S   SHORT  TITLE  CATALOG 

Tidy,  C.  Meymott.     Treatment  of  Sewage.     (Science   Series  No.   94.). 

i6mo,  o  50 

Tinney,  W.  H.    Gold-mining  Machinery 8vo,  *3  oo 

Titherley,  A.  W.     Laboratory  Course  of  Organic  Chemistry 8vo,  *2  oo 

Toch,  M.     Chemistry  and  Technology  of  Mixed  Paints 8vo,  *3  oo 

Materials  for  Permanent  Painting i2mo,  *2  oo 

Todd,  J.,  and  Whall,  W.  B.     Practical  Seamanship 8vo,  *7  50 

Tonge,  J.     Coal.     (Westminster  Series.) 8vo,  *2  oo 

Townsend,  F.     Alternating  Current  Engineering 8vo,  boards  *o  75 

Townsend,  J.     lonization  of  Gases  by  Collision 8vo,  *i  25 

Transactions  of  the  Amerkan  Institute  of  Chemical  Engineers.     8vo. 

Vol.     I.     1908 "-600 

Vol.    II.     1909 *6  oo 

Vol.  IH.     1910 *6  oo 

Vol.  IV.     1911 *6  oo 

Traverse  Tables.     (Science  Series  No.  115.) i6mo,  o  50 

morocco,  i  oo 
Trinks,  W.,  and  Housum,  C.     Shaft  Governors.     (Science  Series  No.  122.) 

i6mo,  o  50 

Trowbridge,  W.  P.     Turbine  Wheels.     (Science  Series  No.  44.) i6mo,  o  50 

Tucker,  J.  H.     A  Manual  of  Sugar  Analysis 8vo,  3  50 

Tumlirz,  O.     Potential.     Trans,  by  D.  Robertson i2mo,  i  25 

Tunner,  P.  A.     Treatise  on  Roll-turning.     Trans,  by  J.  B.  Pearse. 

8vo,  text  and  folio  atlas,  10  oo 

Turbayne,  A.  A.     Alphabets  and  Numerals 4to,  2  oo 

Turnbull,  Jr.,  J.,  and  Robinson,  S.  W.     A  Treatise  on  the  Compound 

Steam-engine,      (Science  Series  No.  8.) i6mo, 

Turrill,  S.  M.     Elementary  Course  in  Perspective i2mo,  *i  25 

Underbill,  C.  R.     Solenoids,  Electromagnets  and  Electromagnetic  Wind- 
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Universal  Telegraph  Cipher  Code i2mo,  i  oo 

Urquhart,  J.  W.     Electric  Light  Fitting i2mo,  2  oo 

Electro-plating i2mo,  2  oo 

Electrotyping i2mo,  2  oo 

Electric  Ship  Lighting i2mo,  3  oo 

Vacher,  F.  Food  Inspector's  Handbook i2mo,  *2  50 

Van  Nostrand's  Chemical  Annual.  Second  issue  1909 i2mo,  *2  50 

Year  Book  of  Mechanical  Engineering  Data.  First  issue  1912  ...(In  Press.) 

Van  Wagenen,  T.  F.  Manual  of  Hydraulic  Mining i6mo,  i  oo 

Vega,  Baron  Von.  Logarithmic  Tables 8vo,  half  morocco,  2  oo 

Villon,  A.  M.  Practical  Treatise  on  the  Leather  Industry.  Trans,  by  F. 

T.  Addyman 8vo,  *io  oo 

Vincent,  C.  Ammonia  and  its  Compounds.  Trans,  by  M.  J.  Salter .  .  8vo,  *2  oo 

Volk,  C.  *  Haulage  and  Winding  Appliances 8vo,  *4  oo 

Von  Georgievics,  G.  Chemical  Technology  of  Textile  Fibres.  Trans,  by 

C.  Salter 8vo,  *4  50 

Chemistry  of  Dyestuffs.  Trans,  by  C.  Salter 8vo,  *4  50 

Vose,  G.  L.  Graphic  Method  for  Solving  Certain  Questions  in  Arithmetic 

and  Algebra.     (Science  Series  No.  16.) i6mo,  o  50 


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Wabner,  R.     Ventilation  in  Mines.     Trans,  by  C.  Salter 8vo,  *4  50 

Wade,  E.  J.     Secondary  Batteries 8vo,  *4  oo 

Wadmore,  T.  M.    Elementary  Chemical  Theory lamo,  *i  50 

Wadsworth,  C.     Primary  Battery  Ignition. I2mo  (In  Press.) 

Wagner,  E.     Preserving  Fruits,  Vegetables,  and  Meat i2mo,  *2  50 

Waldram,  P.  J.      Principles  of  Structural  Mechanics (In  Press.) 

Walker,  F.     Aerial  Navigation 8vo,  2  oo 

Dynamo  Building.     (Science  Series  No.  98.) i6mo,  o  50 

Electric  Lighting  for  Marine  Engineers 8vo,  2  oo 

Walker,  S.  F.     Steam  Boilers,  Engines  and  Turbines 8vo,  3  oo 

Refrigeration,  Heating  and  Ventilation  on  Shipboard i2mo,  *2  oo 

Electricity  in  Mining 8vo,  *3  50 

Walker,  W.  H.     Screw  Propulsion 8vo,  o  75 

Wallis-Tayler,  A.  J.     Bearings  and  Lubrication 8vo,  *i  50 

Aerial  or  Wire  Ropeways 8vo,  *3  oo 

Modern  Cycles 8vo,  4  oo 

Motor  Cars 8vo,  i  80 

Motor  Vehicles  for  Business  Purposes 8vo,  3  50 

Pocket  Book  of  Refrigeration  and  Ice  Making i2mo,  i  50 

Refrigeration,  Cold  Storage  and  Ice-Making 8vo,  *4  50 

Sugar  Machinery i2mo,  *2  oo 

Wanklyn,  J.  A.     Water  Analysis i2mo,  2  oo 

Wansbrough,  W.  D.     The  A  B  C  of  the  Differential  Calculus i2mo,  *i  50 

Slide  Valves i2mo,  *2  oo 

Ward,  J.  H.     Steam  for  the  Million 8vo,  i  oo 

Waring,  Jr.,  G.  E.     Sanitary  Conditions.     (Science  Series  No.  31.). .  i6mo,  o  50 

Sewerage  and  Land  Drainage *6  oo 

Waring,  Jr.,  G.  E.     Modern  Methods  of  Sewage  Disposal i2mo,  2  oo 

How  to  Drain  a  House i2mo,  i  25 

Warren,  F.  D.     Handbook  on  Reinforced  Concrete i2mo,  *2  50 

Watkins,  A.    Photography.     (Westminster  Series.) 8vo,  *2  oo 

Watson,  E.  P.     Small  Engines  and  Boilers I2mo,  i  25 

Watt,  A.     Electro-plating  and  Electro-refining  of  Metals 8vo,  *4  50 

Electro-metallurgy i2mo,  i  oo 

The  Art  of  Soap-making 8vo,  3  oo 

Leather  Manufacture 8vo,  *4  oo 

Paper-Making 8vo,  3  oo 

Weale,  J.     Dictionary  of  Terms  Used  in  Architecture i2mo,  2  50 

Weale's  Scientific  and  Technical  Series.     (Complete  list  sent  on  applica- 
tion.) 

Weather  and  Weather  Instruments i2mo,  i  oo 

paper,  o  50 

Webb,  H.  L.     Guide  to  the  Testing  of  Insulated  Wires  and  Cables. .  i2mo,  i  oo 

Webber,  W.  H.  Y.     Town  Gas.     (Westminster  Series.) 8vo,  *2  oo 

Weisbach,  J.     A  Manual  of  Theoretical  Mechanics 8vo,  *6  oo 

sheep,  *7  50 

Weisbach,  J.,  and  Herrmann,  G.     Mechanics  of  Air  Machinery 8vo,  *3  75 

Welch,  W.     Correct  Lettering (In  Press.) 

Weston,  E.  B.     Loss  of  Head  Due  to  Friction  of  Water  in  Pipes  . . .  i2mo,  *i  50 

Weymouth,  F.  M.     Drum  Armatures  and  Commutators 8vo,  *3  oo 

Wheatley,  O.    Ornamental  Cement  Work (In  Press.) 


28     D.  VAN  NOSTRAND  COMPANY'S  SHORT  TITLE  CATALOG 

Wheeler,  J.  B.     Art  of  War i2mo,  i  75 

Field  Fortifications i2mo,  i  75 

Whipple,  S.     An  Elementary  and  Practical  Treatise  on  Bridge  Building. 

8vo,  3  oo 

Whithard,  P.     Illuminating  and  Missal  Painting i2mo,  i  50 

Wilcox,  R.  M.     Cantilever  Bridges.     (Science  Series  No.  25.) i6mo,  o  50 

Wilkinson,  H.  D.     Submarine  Cable  Laying  and  Repairing 8vo,  *6  oo 

Williams,  A.  D.,  Jr.,  and  Hutchinson,  R.  W.     The  Steam  Turbine (In  Press.} 

Williamson,  J.,  and  Blackadder,  H.  Surveying 8vo,  (In  Press.} 

Williamson,  R.  S.     On  the  Use  of  the  Barometer 4to,  15  oo 

Practical  Tables  in  Meteorology  and  Hypsometery 4to,  2  50 

Willson,  F.  N.     Theoretical  and  Practical  Graphics 4to,  *4  oo 

Wimperis,  H.  E.     Internal  Combustion  Engine 8vo,  *3  oo 

Winchell,  N.  H.,  and  A.  N.     Elements  of  Optical  Mineralogy 8vo,  *3  50 

Winkler,  C.,  and  Lunge,  G.     Handbook  of  Technical  Gas- Analysis ...  8vo,  4  oo 

Winslow,  A.     Stadia  Surveying.     (Science  Series  No.  77.) i6mo,  o  50 

Wisser,   Lieut.   J.   P.     Explosive  Materials.     (Science   Series  No.   70.). 

i6mo,  o  50 

Wisser,  Lieut.  J.  P.     Modern  Gun  Cotton.     (Science  Series  No.  89.)i6mo,  o  50 

Wood,  De  V.     Luminiferous  Aether.     (Science  Series  No.  85.) ....  i6mo,  o  50 
Woodbury,  D.  V.     Elements  of  Stability  in  the  Well-proportioned  Arch. 

8vo,  half  morocco,  4  oo 

Worden,  E.  C.     The  Nitrocellulose  Industry.     Two  Volumes 8vo,  *io  oo 

-  Cellulose  Acetate 8vo,  (In  Press.} 

Wright,  A.  C.     Analysis  of  Oils  and  Allied  Substances 8vo,  *3  50 

Simple  Method  for  Testing  Painters'  Materials 8vo,  *2  50 

Wright,  F.  W.     Design  of  a  Condensing  Plant i2mo,  *i  50 

Wright,  H.  E.     Handy  Book  for  Brewers 8vo,  •  *s  oo 

Wright,  J.     Testing,  Fault  Finding,  etc.,  for  Wiremen.      (Installation 

Manuals  Series.) i6mo,  *o  50 

Wright,  T.  W.     Elements  of  Mechanics 8vo,  *2  50 

Wright,  T.  W.,  and  Hayford,  J.  F.     Adjustment  of  Observations 8vo,  *3  oo 

Young,  J.  E.     Electrical  Testing  for  Telegraph  Engineers 8vo,  *4  oo 

Zahner,  R.     Transmission  of  Power.     (Science  Series  No.  40.) ....  i6mo, 

Zeidler,  J.,  and  Lustgarten,  J.     Electric  Arc  Lamps 8vo,  *2  oo 

Zeuner,  A.     Technical  Thermodynamics.     Trans,  by  J.  F.  Klein.     Two 

Volumes 8vo,  *8  oo 

Zimmer,  G.  F.     Mechanical  Handling  of  Material 4to',  *io  oo 

Zipser,  J.    Textile  Raw  Materials.     Trans,  by  C.  Salter 8vo,  *s  oo 

Zur  Nedden,  F.     Engineering  Workshop  Machines  and  Processes.     Trans. 

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